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【330039】16.2 二次根式的乘除(3)

时间:2025-02-07 09:19:33 作者: 字数:2484字

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

16.2 二次根式的乘除(3)

课型: 上课时间: 课时:

学习内容

最简二次根式的概念及利用最简二次根式的概念进行二次根式的化简运算.

学习目标

理解最简二次根式的概念,并运用它把不是最简二次根式的化成最简二次根式.

学习过程

  1. 自主学习

(一)复习引入

1.计算(1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =,(2 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =,(3 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =

2.现在我们来看本章引言中的问题:如果两个电视塔的高分别是h1kmh2km那么它们的传播半径的比是_________

(二)、探索新知

观察上面计算题1的最后结果,可以发现这些式子中的二次根式有如下两个特点:

1.被开方数不含分母;

2.被开方数中不含能开得尽方的因数或因式.

我们把满足上述两个条件的二次根式,叫做最简二次根式.

那么上题中的比是否是最简二次根式呢?如果不是,把它们化成最简二次根式.

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> == <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

1.化简:(1)  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ; (2)  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ; (3)  <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

= = =

2.如图,在Rt△ABC中,∠C=90°AC=2.5cmBC=6cm,求AB的长.

二、巩固练习

教材练习

三、学生小组交流解疑,教师点拨、拓展

1观察下列各式,通过分母有理数,把不是最简二次根式的化成最简二次根式:

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> -1

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> - <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

同理可得: <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> - <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,……

从计算结果中找出规律,并利用这一规律计算

 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +…… <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )( <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +1)的值.

=

2、归纳小结

1).重点:最简二次根式的运用.

2).难点关键:会判断这个二次根式是否是最简二次根式.

四、课堂检测

(一)、选择题

1.将 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y>0)化为最简二次根式是( ).

A <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y>0B <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y>0C <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y>0D.以上都不对

2.把(a-1 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中根号外的(a-1)移入根号内得( ).

A <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3.化简 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是( ) A- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D- <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

二、填空题 1.化简 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_________.(x≥0

2a <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简二次根式号后的结果是_________

三、综合提高题

xy为实数,且y= <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求 <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值.