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【330465】初中数学人教八下第十六章卷(2)

时间:2025-02-09 11:32:48 作者: 字数:12628字

第十六章卷(2

一、选择题

1.下列各式中,正确的是(  )

A2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 3 B3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 4 C4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 5 D14 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 16


2.下列二次根式中,是最简二次根式的是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


3.把二次根式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0)化为最简二次根式结果是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 D.以上都不对


4.以下二次根式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 中,与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的被开方数相同的是(  )

A B C D


5.化简:a <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的结果是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C.﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D.﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


6.当a0时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 中,比较它们的结果,下面四个选项中正确的是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


二、填空题

7.下列各式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0)、 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 、﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0y0)中    是二次根式.


8.当x   时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 在实数范围内有意义.


9.化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   .(x0


10.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   


11.若n0,则代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =  


12.实数a在数轴上的位置如图所示,则|a﹣1|+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


13.若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +y2﹣4y+4=0,则xy的值为   


14  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的有理化因式是  


三、解答题

15.计算:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(3) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(4) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> );

(5)3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> );

(6)3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2

(7) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(8) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


16.先化简,再求值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,其中x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y=27


17.解方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x﹣1= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x+1


18.先阅读下列的解答过程,然后作答:

形如 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的化简,只要我们找到两个数ab使a+b=mab=n,这样( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2=m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,那么便有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ± <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ab)例如:化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

解:首先把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 化为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,这里m=7n=12

由于4+3=74×3=12,即( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2=7 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

由上述例题的方法化简:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(3) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>











答案

1.下列各式中,正确的是(  )

A2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 3 B3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 4 C4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 5 D14 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 16

【考点】二次根式的定义.

【专题】选择题.

【分析】首先估算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的整数部分和小数部分,再比较大小即可求解.

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 3.8733.874

3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 4

故选B

【点评】本题考查了同学们对无理数大小的估算能力,比较简单.


2.下列二次根式中,是最简二次根式的是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】最简二次根式.

【专题】选择题.

【分析】A选项中含有小数;D选项的被开方数中含有能开得尽方的因数;C选项的被开方数中含有分母;

因此这三个选项都不符合最简二次根式的要求.所以本题的答案应该是B

【解答】解:A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不是最简二次根式;

B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不含有未开尽方的因数或因式,是最简二次根式;

C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,被开方数中含有分母,故不是最简二次根式;

D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不是最简二次根式.

只有选项B中的是最简二次根式,故选B

【点评】在判断最简二次根式的过程中要注意:

(1)在二次根式的被开方数中,只要含有分数或小数,就不是最简二次根式;

(2)在二次根式的被开方数中的每一个因式(或因数),如果幂的指数大于或等于2,也不是最简二次根式.


3.把二次根式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0)化为最简二次根式结果是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y0 D.以上都不对

【考点】最简二次根式.

【专题】选择题.

【分析】根据最简二次根式的被开方数不含开的尽的因数或因式,被开方数不含分母,可得答案.

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故选C

【点评】本题考查了最简二次根式,利用了二次根式的除法.


4.以下二次根式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 中,与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的被开方数相同的是(  )

A B C D

【考点】被开方数相同的最简二次根式.

【专题】选择题.

【分析】先把每个二次根式化为最简二次根式,然后根据被开方数相同的最简二次根式的定义解答.

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的被开方数相同的是

故选C

【点评】本题考查了被开方数相同的最简二次根式的定义.


5.化简:a <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的结果是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C.﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D.﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的性质与化简.

【专题】选择题.

【分析】直接利用二次根式的性质得出a的符号,进而化简求出即可.

【解答】解:由题意可得:a0

a <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故选C

【点评】此题主要考查了二次根式的性质与化简,正确得出a的符号是解题关键.


6.当a0时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 中,比较它们的结果,下面四个选项中正确的是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的性质.

【专题】选择题.

【分析】首先根据二次根式的性质可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 0,而﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 0,进一步得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,由此选择答案即可.

【解答】解:由分析可知当a0时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故选A

【点评】此题考查实数的大小比较,掌握二次根式的性质与计算是解答的前提.


7.下列各式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0)、 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 、﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0y0)中    是二次根式.

【考点】二次根式的定义.

【专题】填空题.

【分析】根据二次根式的定义进行解答即可.

【解答】解:二次根式是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0)、﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x0y0),

故答案为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 、﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的定义,掌握二次根式有意义的条件是解题的关键.


8.当x   时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 在实数范围内有意义.

【考点】二次根式有意义的条件.

【专题】填空题.

【分析】二次根式的被开方数是非负数.

【解答】解:当3x﹣10,即x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 在实数范围内有意义.

故答案为:x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】考查了二次根式的意义和性质.概念:式子 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> a0)叫二次根式.性质:二次根式中的被开方数必须是非负数,否则二次根式无意义.


9.化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   .(x0

【考点】二次根式的性质与化简.

【专题】填空题.

【分析】原式利用二次根式的性质化简即可得到结果.

【解答】解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故答案为:x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】此题考查了二次根式的性质与化简,熟练掌握运算法则是解本题的关键.


10.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

【考点】二次根式的混合运算.

【专题】填空题.

【分析】利用二次根式的除法法则运算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ; 利用二次根式的乘除法则运算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =;利用分母有理化计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> );利用二次根式的除法法则运算  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故答案为﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的混合运算:先把各二次根式化简为最简二次根式,然后进行二次根式的乘除运算,再合并即可.


11.若n0,则代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =  

【考点】二次根式的性质与化简.

【专题】填空题.

【分析】首先写成 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的形式,然后分别进行化简即可.

【解答】解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> •m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> (﹣n

=﹣3mn <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故答案是:﹣3mn <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的化简,关键是理解二次根式的性质: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =|a|


12.实数a在数轴上的位置如图所示,则|a﹣1|+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =   

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的性质与化简;实数与数轴.

【专题】填空题.

【分析】根据数轴上表示的两个数,右边的数总比左边的大,分别得出a﹣10a﹣20的关系,然后根据绝对值的意义和二次根式的意义化简.

【解答】解:根据数轴上显示的数据可知:1a2

a﹣10a﹣20

|a﹣1|+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =a﹣1+2﹣a=1

故答案为:1

【点评】本题主要考查了数轴,绝对值的意义和根据二次根式的意义化简.

二次根式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的化简规律总结:当a0时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =a;当a0时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣a


13.若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +y2﹣4y+4=0,则xy的值为   

【考点】二次根式的性质.

【专题】填空题.

【分析】首先配方,进而利用二次根式的性质以及偶次方的性质,进而得出关于xy的方程组求出即可.

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +y2﹣4y+4=0

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +y﹣22=0

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

xy的值为:4

故答案为:4

【点评】此题主要考查了配方法应用以及偶次方的性质和二次根式的性质等知识,正确配方是解题关键.


14  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的有理化因式是  

【考点】二次根式的混合运算.

【专题】填空题.

【分析】根据平方差公式即可得出( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣1,再结合有理化因式的定义即可得出结论.

【解答】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2﹣3=﹣1

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的一个有理化因式.

故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了平方差公式以及有理化因式的定义,根据平方差公式找出( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =﹣1是解题的关键.


15.计算:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(3) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(4) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> );

(5)3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> );

(6)3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2

(7) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(8) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的混合运算.

【专题】解答题.

【分析】(1)先把各二次根式化简为最简二次根式,然后合并即可;

(2)利用二次根式的乘除法则运算;

(3)先把各二次根式化简为最简二次根式,然后合并即可;

(4)利用二次根式的乘法法则运算;

(5)利用多项式乘法展开,然后合并即可;

(6)利用完全平方公式计算;

(7)利用二次根式的乘除法则运算和平方差公式计算;

(8)利用二次根式的乘除法则运算和平方差公式计算.

【解答】解:(1)原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2)原式=1× <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=10

(3)原式=3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(4)原式=﹣ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=﹣4+6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(5)原式=18﹣9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣12

=6﹣5 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(6)原式=54﹣18 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +15

=69﹣18 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(7)原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3﹣1

=3+2

=5

(8)原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=4+2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的混合运算:先把各二次根式化简为最简二次根式,然后进行二次根式的乘除运算,再合并即可.在二次根式的混合运算中,如能结合题目特点,灵活运用二次根式的性质,选择恰当的解题途径,往往能事半功倍


16.先化简,再求值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,其中x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y=27

【考点】二次根式的混合运算.

【专题】解答题.

【分析】首先对二次根式进行化简,然后去括号、合并二次根式即可化简,然后把xy的值代入求解.

【解答】解:原式=6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )﹣( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> y=27时,

原式=3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的化简求值,正确对二次根式进行化简是关键.


17.解方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x﹣1= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x+1

【考点】二次根式的混合运算.

【专题】解答题.

【分析】根据一元一次方程的解法求解.

【解答】解:移项得:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

解得:x=5+2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的应用,解答本题的关键是掌握一元一次方程的解法.


18.先阅读下列的解答过程,然后作答:

形如 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的化简,只要我们找到两个数ab使a+b=mab=n,这样( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2=m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,那么便有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ± <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ab)例如:化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

解:首先把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 化为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,这里m=7n=12

由于4+3=74×3=12,即( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2=7 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

由上述例题的方法化简:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(3) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的混合运算.

【专题】解答题.

【分析】先把各题中的无理式变成 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 的形式,再根据范例分别求出各题中的ab,即可求解.

【解答】解:(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(3) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】主要考查二次根式根号内含有根号的式子化简.根据二次根式的乘除法法则进行二次根式根号内含有根号的式子化简.二次根式根号内含有根号的式子化简主要利用了完全平方公式,所以一般二次根式根号内含有根号的式子化简是符合完全平方公式的特点的式子.