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【330729】二次根式单元测试

时间:2025-02-11 18:40:06 作者: 字数:19722字


【章节测验训练】第16 二次根式

 

一、选择题(共9小题)

1.(2014•白银)下列计算错误的是(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2

D

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

2.(2014•保定二模)等腰三角形的两条边长分别为2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,那么这个三角形的周长为(  )

 

A

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

3.(2014•张家港市模拟)已知实数xy满足x+y=﹣2axy=aa≥1),则 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a

B

2a <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

a <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

4.(2014•济宁)如果ab0a+b0,那么下面各式:① <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,② <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =1,③ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =﹣b,其中正确的是(  )

 

A

①②

B

②③

C

①③

D

①②③

 

5.(2013•台湾)kmn为三整数,若 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =k <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =15 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =6 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则下列有关于kmn的大小关系,何者正确?(  )

 

A

km=n

B

m=nk

C

mnk

D

mkn

 

6.(2013•衡阳)计算 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果为(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

3

D

5

 

7.(2014•洪山区三模)下列式子中正确的是(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

8.(2013•景德镇二模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =(  )

 

A

5

B

1

C

3

D

3

 

9.(2014•丰润区二模)已知a为实数,则代数式 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的最小值为(  )

 

A

0

B

3

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

9

 

二、填空题(共4小题)(除非特别说明,请填准确值)

10.(2014•丹东)若式子 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,则实数x的取值范围是 _________ 

11.(2014•凉山州)已知x1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x2= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则x12+x22= _________ 

 

12.(2014•镇江)读取表格中的信息,解决问题.

n=1

a1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

b1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2

c1=1+2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

n=2

a2=b1+2c1

b2=c1+2a1

c2=a1+2b1

n=3

a3=b2+2c2

b3=c2+2a2

c=a2+2b2

满足 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>n可以取得的最小整数是 _________ 

 

13.(2014•白银)已知xy为实数,且y= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +4,则x﹣y= _________ 

 

三、解答题(共7小题)(选答题,不自动判卷)

14.(2014•凉山州)计算:( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2﹣6sin30°﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>0+ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +| <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> |

 

15.(2013•甘井子区一模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

16.(2013•嘉定区二模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

17.(2013•沙河口区一模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

18.(2012•巴中)先化简,再求值:( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )• <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,其中x= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 

19.(2013•金湾区一模)观察下列各式及证明过程:(1 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;(2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;(3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

a.按照上述等式及验证过程的基本思想,猜想 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的变形结果并进行验证;

b.针对上述各式反映的规律,写出用nn≥1的自然数)表示的等式,并验证.

 

20.(2013•湖州模拟)化简求值: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,其中 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


【章节训练】第16 二次根式

参考答案与试题解析

 

一、选择题(共9小题)

1.(2014•白银)下列计算错误的是(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2

D

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的混合运算.菁优网版权所有

分析:

利用二次根式的运算方法逐一算出结果,比较得出答案即可.

解答:

解:A <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,计算正确;

B <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,不能合并,原题计算错误;

C <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2,计算正确;

D <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,计算正确.

故选:B

点评:

此题考查二次根式的运算方法和化简,掌握计算和化简的方法是解决问题的关键.

 

2.(2014•保定二模)等腰三角形的两条边长分别为2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,那么这个三角形的周长为(  )

 

A

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

4 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的应用.菁优网版权所有

分析:

等腰三角形的边可能是腰,也可能是底边,因而本题应分两种情况讨论:①腰长为2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;②腰长为5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .进行讨论,看是否满足三角形的三边关系,不满足的舍去,满足的算出三角形的周长即可.

解答:

解:①若腰长为2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则有2×2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,故此情况不合题意,舍去;

若腰长为5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则三角形的周长=2×5 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =10 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:B

点评:

此题主要考查了实数的运算、三角形的三边关系及等腰三角形的性质,解决本题的关键是注意对等腰三角形的边进行讨论.

 

3.(2014•张家港市模拟)已知实数xy满足x+y=﹣2axy=aa≥1),则 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a

B

2a <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

a <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的化简求值.菁优网版权所有

分析:

首先根据已知条件可以判断出xy均为负数,然后根据二次根式的性质化简 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,再进一步代入求得数值即可.

解答:

解:∵x+y=﹣2axy=aa≥1),

xy均为负数,

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 0

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:D

点评:

此题考查二次根式的化简求值,注意先化简再求值.

 

4.(2014•济宁)如果ab0a+b0,那么下面各式:① <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,② <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =1,③ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =﹣b,其中正确的是(  )

 

A

①②

B

②③

C

①③

D

①②③


考点

二次根式的乘除法.菁优网版权所有

专题

计算题.

分析:

ab0a+b0先求出a0b0,再进行根号内的运算.

解答:

解:∵ab0a+b0

a0b0

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,被开方数应≥0ab不能做被开方数,(故①错误),

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =1 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =1,(故②正确),

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =﹣b <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =﹣b,(故③正确).

故选:B

点评:

本题是考查二次根式的乘除法,解答本题的关键是明确a0b0

 

5.(2013•台湾)kmn为三整数,若 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =k <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =15 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =6 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则下列有关于kmn的大小关系,何者正确?(  )

 

A

km=n

B

m=nk

C

mnk

D

mkn


考点

二次根式的性质与化简.菁优网版权所有

专题

计算题.

分析:

根据二次根式的化简公式得到kmn的值,即可作出判断.

解答:

解: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =15 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =6 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

可得:k=3m=2n=5

mkn

故选D

点评:

此题考查了二次根式的性质与化简,熟练掌握二次根式的化简公式是解本题的关键.

 

6.(2013•衡阳)计算 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果为(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

3

D

5


考点

二次根式的乘除法;零指数幂.菁优网版权所有

专题

计算题.

分析:

原式第一项利用二次根式的乘法法则计算,第二项利用零指数幂法则计算,即可得到结果.

解答:

解:原式=2+1=3

故选C

点评:

此题考查了二次根式的乘除法,以及零指数幂,熟练掌握运算法则是解本题的关键.

 

7.(2014•洪山区三模)下列式子中正确的是(  )

 

A

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的加减法.菁优网版权所有

分析:

根据二次根式的运算法则分别计算,再作判断.

解答:

解:A、不是同类二次根式,不能合并,故错误;

BD、开平方是错误的;

C、符合合并同类二次根式的法则,正确.

故选C

点评:

同类二次根式是指几个二次根式化简成最简二次根式后,被开方数相同的二次根式.

二次根式的加减运算,先化为最简二次根式,再将被开方数相同的二次根式进行合并.

 

8.(2013•景德镇二模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =(  )

 

A

5

B

1

C

3

D

3


考点

二次根式的加减法;实数的运算.菁优网版权所有

分析:

同类二次根式:①根指数是2,②被开数相同.二次根式的加减运算,只有同类二次根式才能合并.注意 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3

解答:

解:2﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2﹣3=﹣1

故选B

点评:

考查二次根式的加减运算,先化简,再合并.

 

9.(2014•丰润区二模)已知a为实数,则代数式 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的最小值为(  )

 

A

0

B

3

C

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D

9


考点

二次根式的性质与化简.菁优网版权所有

专题

压轴题.

分析:

把被开方数用配方法整理,根据非负数的意义求二次根式的最小值.

解答:

解:∵原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

当(a﹣32=0,即a=3

代数式 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值最小,为 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>3

故选B

点评:

用配方法对多项式变形,根据非负数的意义解题,是常用的方法,需要灵活掌握.

 

二、填空题(共4小题)(除非特别说明,请填准确值)

10.(2014•丹东)若式子 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,则实数x的取值范围是 x≤2x≠0 


考点

二次根式有意义的条件;分式有意义的条件.菁优网版权所有

专题

计算题.

分析:

根据被开方数大于等于0,分母不等于0列式计算即可得解.

解答:

解:由题意得,2﹣x≥0x≠0

解得x≤2x≠0

故答案为:x≤2x≠0

点评:

本题考查的知识点为:分式有意义,分母不为0;二次根式的被开方数是非负数.

 

11.(2014•凉山州)已知x1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x2= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则x12+x22= 10 


考点

二次根式的混合运算.菁优网版权所有

分析:

首先把x12+x22=x1+x22﹣2x1x2,再进一步代入求得数值即可.

解答:

解:∵x1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x2= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x12+x22

=x1+x22﹣2x1x2

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2﹣2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=12﹣2

=10

故答案为:10

点评:

此题考查二次根式的混合运算,把代数式利用完全平方公式化简是解决问题的关键.

 

12.(2014•镇江)读取表格中的信息,解决问题.

n=1

a1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

b1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2

c1=1+2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

n=2

a2=b1+2c1

b2=c1+2a1

c2=a1+2b1

n=3

a3=b2+2c2

b3=c2+2a2

c=a2+2b2

满足 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>n可以取得的最小整数是 7 


考点

二次根式的应用.菁优网版权所有

专题

新定义.

分析:

由表格可知当n=1时,a1+b1+c1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2+1+2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),同理得出a2+b2+c2=9 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),…由此得出an+bn+cn=3n <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),进一步整理 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求得n的最小值即可.

解答:

解:由a1+b1+c1= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2+1+2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),

a2+b2+c2=9 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),

an+bn+cn=3n <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

an+bn+cn≥2014× <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1)( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2014 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1),

3n≥2014

36201437

n最小整数是7

故答案为:7

点评:

此题考查二次根式的运用,注意找出运算的规律,进一步利用估算的方法找出解决问题的方法.

 

13.(2014•白银)已知xy为实数,且y= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +4,则x﹣y= ﹣1或﹣7 


考点

二次根式有意义的条件.菁优网版权所有

专题

计算题.

分析:

根据一对相反数同时为二次根式的被开方数,那么被开方数为0可得x可能的值,进而得到y的值,相减即可.

解答:

解:由题意得x2﹣9=0

解得x=±3

y=4

x﹣y=﹣1或﹣7

故答案为﹣1或﹣7

点评:

考查二次根式有意义的相关计算;得到x可能的值是解决本题的关键;用到的知识点为:一对相反数同时为二次根式的被开方数,那么被开方数为0

 

三、解答题(共7小题)(选答题,不自动判卷)

14.(2014•凉山州)计算:( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2﹣6sin30°﹣ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>0+ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +| <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> |


考点

二次根式的混合运算;零指数幂;负整数指数幂;特殊角的三角函数值.菁优网版权所有

专题

计算题.

分析:

先算负指数幂,特殊角的三角函数值,0指数幂,以及绝对值,再算乘法,最后算加减,由此顺序计算即可.

解答:

解:原式=4﹣6× <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ﹣1+ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=4﹣3﹣1+ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

点评:

此题考查负指数幂,特殊角的三角函数值,0指数幂,以及绝对值,二次根式的混合运算,按照运算顺序,正确判定符号计算即可.

 

15.(2013•甘井子区一模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的混合运算;负整数指数幂.菁优网版权所有

专题

计算题.

分析:

原式第一项利用平方差公式化简,第二项利用负指数幂法则计算,最后一项利用平方根的定义化简,即可得到结果.

解答:

解:原式=5﹣4+4﹣5=0

点评:

此题考查了二次根式的混合运算,以及负指数幂运算,熟练掌握法则是解本题的关键.

 

16.(2013•嘉定区二模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的混合运算;零指数幂;特殊角的三角函数值.菁优网版权所有

专题

计算题.

分析:

原式第一项利用零指数幂法则计算,第二项化为最简二次根式,第三、四项利用特殊角的三角函数值化简,即可得到结果.

解答:

解:原式=1﹣3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +4× <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=1﹣3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ﹣2+ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣1

点评:

此题考查了二次根式的混合运算,熟练掌握运算法则是解本题的关键.

 

17.(2013•沙河口区一模)计算: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的混合运算;负整数指数幂.菁优网版权所有

专题

计算题.

分析:

原式第一项利用平方差公式化简,第二项化为最简二次根式,最后一项利用负指数幂法则计算,即可得到结果.

解答:

解:原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2﹣1+2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ﹣3=2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ﹣1

点评:

此题考查了二次根式的混合运算,以及负指数幂运算,熟练掌握法则是解本题的关键.

 

18.(2012•巴中)先化简,再求值:( <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )• <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,其中x= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的化简求值;分式的化简求值.菁优网版权所有

专题

压轴题;分类讨论.

分析:

先根据分式混合运算的法则把原式进行化简,再把x的值代入进行计算即可.

解答:

解:原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,x+10

可知 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =x+1

故原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

点评:

本题考查的是二次根式及分式的化简求值,解答此题的关键是当x= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时得出 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =x+1,此题难度不大.

 

19.(2013•金湾区一模)观察下列各式及证明过程:(1 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;(2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;(3 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

a.按照上述等式及验证过程的基本思想,猜想 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的变形结果并进行验证;

b.针对上述各式反映的规律,写出用nn≥1的自然数)表示的等式,并验证.


考点

二次根式的性质与化简.菁优网版权所有

专题

规律型.

分析:

应用二次根式的性质对二次根式变形,首先应注意变形的规律.

解答:

解:(1 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

点评:

本题主要考查二次根式的变形,二次根式的性质运用:a0时, <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =aa0时, <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =﹣aa=0时, <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =0

 

20.(2013•湖州模拟)化简求值: <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,其中 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


考点

二次根式的化简求值;分式的化简求值.菁优网版权所有

分析:

先把分式化简:把分子、分母能分解因式的分解,能约分的约分,然后先除后减,化简为最简形式,最后把a的值代入计算.

解答:

解:原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,

原式= <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

点评:

此题考查分式的化简与求值,主要的知识点是因式分解、通分、约分等.