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【330038】16.2 二次根式的乘除(2)

时间:2025-02-07 09:19:24 作者: 字数:2046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>

162 二次根式的乘除(2

课型: 上课时间: 课时:

学习内容:

 <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≥0b>0),反过来 <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≥0b>0)及利用它们进行计算和化简.

学习目标:

理解 <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≥0b>0)和 <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≥0b>0)及利用它们进行运算.

教学过程

  1. 自主学习

(一)复习引入

1.写出二次根式的乘法规定及逆向等式.

2.填空

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> =____; 规律:  <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>

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> =____ <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>

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> =____ <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>

4 <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>

(二)、探索新知

一般地,对二次根式的除法规定:

 <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≥0b>0反过来, <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≥0b>0

下面我们利用这个规定来计算和化简一些题目.

二、巩固练习

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> 4 <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> 4 <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、巩固练习

教材练习.

三、学生小组交流解疑,教师点拨、拓展

1、 例3已知 <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> ,且x为偶数,求(1+x <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.

2、归纳小结

1)本节课要掌握 <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≥0b>0)和 <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≥0b>0)及其运用.

并利用它们进行计算和化简.

四、课堂检测

(一)、选择题

1.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> 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>  <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>

2.阅读下列运算过程: <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>

数学上将这种把分母的根号去掉的过程称作“分母有理化”,请化简 <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( ).

A2 B6 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>  <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.分母有理化:(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.已知x=3y=4z=5,那么 <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> 的最后结果是_______

三、综合提高题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> m>0n>0