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【330036】16.2 第2课时 二次根式的除法

时间:2025-02-07 09:19:17 作者: 字数:3613字

16.2 二次根式的乘除

2课时 二次根式的除法

一、选择题

1.下列计算不正确的是( )

A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2.下列各式中,最简二次根式是( )

A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3.(易错题)下列各式错误的是(

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

4. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 立的条件是(

A. x≥0 B. x<1

C. 0 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ≤x<1 D.x≥0x <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ≠1

5.下列二次根式是最简二次根式的是(

A.  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ; C.  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

6.化简 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是( )

A.  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

7.计算 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是(

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


二、填空题

8.在横线上填出一个最简单的因式,使得它与所给二次根式相乘的结果为有理式,如: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ (2) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ____ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> __

(3) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ (4) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ (5) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______

9.化简二次根式:(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ________(2) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> _________(3) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> _________

10.已知 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> _________(结果精确到0001)

11.如果 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 用含a,b的代数式表示为__________ .[来源:__]

三、解答题

12.计算:

1 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

13.已知a,b满足 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值.

14.观察下列各 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 式及其验证过程:

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

验证: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

1)按照上述两个等式及其验证过程的基本思路,猜想 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的变形结果并进行 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 验证;

(2)针对上述各式反映的规律,写出用n(n为自然数,且n <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ≥2)表示的等式,并给出证明.


15.已知 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,且x为偶数,求 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值.



16.在进行二次根式化简时,我们有时会碰上如 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 这样的式子,其实我们还可以将其进一步化简:

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

(一) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(二) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> [来源:学科网ZXXK]

(三)以上这种化简的方法叫做分母有理化。

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 还可以用如下方法化简:

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(四)(1)请用不同的方法化简 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

参照(三)式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简;参照(四)式化简.

化简: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .


参考答案

1C

2C

3.C解析 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,A项正确; <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,B项正确; <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,C项错误; <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,D项正确.

4.C解析 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以0≤x1.

5.B解析 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 都不是最简二次根式,只有选项B中被开方数既不含分母,也不含能开得尽方的因数或因式,因此,是最简二次根式.

6.B 解析采用分解质因数的方法,可将20拆成4×5,4可化

22,2022×5,所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

7.B 解析原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,B正确.

8 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

9 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

100.5775.196

11.10ab解析 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .因为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

12.分析: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 可以推广到多个二次根式相乘, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

:(1)原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(2)原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

13.: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 可知

4a-b10, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,

解得a-1,b-3

所以原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

14.思路建立要猜想 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的变形结果及这些式子反 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 映的规律,就需要先对变形后等号两边的式子的结构特点进行观察、比较,归纳出一般规律,再根据题中给出的两个式子的验证方法对猜想、归纳得出的式子进行验证.

:(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

验证: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(2) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (n <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为自然数,n≥2).

证明: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

1 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5.思想建立强要求代数式的值,就需要求出x的值,先根据已知条件得出x的取值范围,再根据x为偶数求出x具体的值,最后将得到的x的值,代入 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简后的代数式中求出最后结果.

:由已知得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

∵x为偶数,x8.

16.思路建立(1)要参照()式化简 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,就需要找一个与 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 相乘能化去根号的式子,即分子 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 、分母同时乘以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 即可.要参照()式化简 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,就需把分子2写成5-3,进而写成 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,再因式分解即可.[来源:**]

(2)参照(1)题的方法, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,…分母有理化,再合并即可.

:(1)原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> [来源:§§Z§X§X§K]

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

(2)原式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>