当前位置:首页 > 八年级 > 数学试卷

【323304】2023八年级数学上册 第5章 二次根式检测题(含解析)(新版)湘教版

时间:2025-01-15 20:30:40 作者: 字数:5185字
简介:


5章 二次根式检测题

(本检测题满分:100分,时间:90分钟)

一、选择题(每小题3分,共24分)

1. 如果代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,那么 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的取值范围是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2.如果 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,那么( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3. 如果最简二次根式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能够合并,那么 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为( )

A.2 B.3 C.4 D.5

4.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

5.下列各式计算正确的是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

6.等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 成立的条件是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

7. 2015·安徽中考)计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B.4  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D.2

8.下列说法正确的是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C.不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的解集为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D.如果分式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 都扩大为原来的3倍,那么分式的值扩大为原来的3

二、填空题(每小题3分,共24分)

9.化简: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_________.

10.比较大小: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

11.1)(2015·湖北黄冈中考)计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =

2)(2015·南京中考)计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是 .

12.2015·南京中考)若式子 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 在实数范围内有意义,则x的取值范围是 .

13.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为两个连续的整数, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

14.(广东中考)若实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 满足| <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2|+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =0,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = .

15.若实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 满足 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为 .

16.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为有理数, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 分别表示 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的整 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 数部分和小数部分, 且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

三、解答题(共52分)

17.6分)计算:(1)(2015·山东临沂中考)计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

18.6分)先化简,再求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

19.6分)先化简,再求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

20.6分)已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求下列代数式的值:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (2) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

21.6分)一个三角形的三边长分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

1)求它的周长(要求结果化简);

2)请你给出一个适当的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 值,使它的周长为整数,并求出此时三角形周长的值.

22.6分)已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为等腰三角形的两条边长,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 满足 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求此三角形的周长.

23.8分)阅读下面问题:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

1)求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值;(2)求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为正整数)的值;

3)计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

24.8分)小明在学习二次根式后,发现一些含根号的式子可以写成另一个式子 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的平方,如: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,善于思考的小明进行了一下探索:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 均为正整数),则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

这样小明就找到一种把部分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的式子化作平方式的方法.
请仿照小明的方法探索并解决下列问题:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 均为正整数时,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
用含有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的式子分别表示 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ______ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> __________.

2)利用所探索的结论,找一组正整数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 填空:

____+_____ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =(_____+_____ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>.(答案不唯一)

3)若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 均为正整数,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值.









5章 二次根式检测题参考答案

1.C 解析:由题意可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

2.B 解析:由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

3.D 解析:由最简二次根式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能够合并,知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

同类二次根式,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

4.A  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 解析:由题意 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

5.C 解析:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以选项A不正确;因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 不是同类二次根

式,不能合并,所以选项B不正确;选项C正确;因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以选项D

正确.

6.C 解析:由题意,知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

7.B 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> × <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =4.

8.B 解析:对于选项A, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;对于选项C, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

对于选项D,分式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 都扩大为原来的3倍,分式的值不变.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 9. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

10.>,< 解析:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

11.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

(2) 5 解析:  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

12. x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1解析:式子 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 在实数范围内有意义的条件是x+1≥0,解得x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 13.-1 解析:由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

14.1 解析:因为| <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2|+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =0,| <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2|≥0 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>0,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=0, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> -4=0,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =4代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =1.

点拨:若两个非负数的和为零,则这两个非负数均等于0.

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 解析:由题意知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

16.2.5 解析:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的整数部分是2,小数部分是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

整理,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为有理数,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

17.解:(1)方法一: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= [ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ][ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ]

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

方法二: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

18.解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

19.解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

所以原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

20.解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

21.解:(1)周长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

2)当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,周长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .(答案不唯一,只要符合题意即可)

22. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> :由题意可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

当腰长为3时,三角形的三边长分别为3,3,4,周长为10

当腰长为4时,三角形的三边长分别为4,4,3,周长为11.

23.解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

24.解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

221,12,3,2(答案不唯一)

3)由题意,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 为正整数,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .





6