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【330040】16.2.1 第1课时 二次根式的乘法

时间:2025-02-07 09:19:30 作者: 字数:1837字

16.2 二次根式的运算

  1. 二次根式的乘除

1课时 二次根式的乘法

一、选择题

1.下列计算正确的是()[来源:学科网ZXXK][来源:,,Z,X,X,K]

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2.( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 易错题)等式 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 成立的条件是(

A.a≤-2a≥2 B. a≥2

C. a≥-2 D. -2≤a≤2

3.(易错題)对于任意实数a,下列各式中一定成立的是(

A. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

4.下列计算正确的是( )

A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

5.如果 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,那么( )

Ax≥0 Bx <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 C0≤x≤3 Dx为任意实数

6.当x=3时, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值是( )

A±3 B3 C.-3 D9

二、填空题

7.化简: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = ;

(2)  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = x≥0y≥0

8.—个长方形的长和宽分别是 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> cm,则这个长方形的面积是 .


三、解答题

9.计算:(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (2) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (3) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


(4) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (5) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (6) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

[来源:学科网ZXXK]

(7) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (8) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (9)  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


10.已知三角形一边长为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,这条边上的 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 高为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求该三角形的面积.


11.化简:

1 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


4 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


12.比较 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的大小.


参考答案

1.D 解析因为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .D正确.

2.B  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 解析由积的算术平方根成立的条件知 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>a≥2,故选B.

3.D 解析A中不 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能保证a-1≥O,a1≥O,所以A不正确;B <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,B不正确;C <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,C不正确;因为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以D正确.

4B

5B

6B

7. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解析① <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

②∵x0 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

8.25cm2解析 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

9(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (2)45 (3)24 (4) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (5) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(6) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (7) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 49 (8)12 (9) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

10 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

11 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .:(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> [来源:Z*xx*k.Com]

(3) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(4) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(5) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

12.分析:可将根号外的因式移到根号里面,然后比较被开方数的大小.

: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,[来源:Zxxk.Com]

又∵4524, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .