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【330033】16.1 二次根式(3)

时间:2025-02-07 09:19:00 作者: 字数:2383字

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

161 二次根式(3)学案

课型: 上课时间: 课时:

学习内容:  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> aa≥0

学习目标:

1、理解 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =aa≥0)并利用它进行计算和化简.

2、通过具体数据的解答,探究 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =aa≥0),并利用这个结论解决具体问题.

教学过程

一、自主学习

(一)、复习引入

1.形如 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)的式子叫做二次根式;

2 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0)是一个非负数; 3( <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )2aa≥0).

那么,我们猜想当a≥0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a是否也成立呢?下面我们就来探究这个问题.

(二)、自主学习

学生学习课本知识

(三)、探究新知

1、填空:根据算术平方根的意义,

 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =__  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_ _  <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =___

2 重点: <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =aa≥0

1 化简

1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解:(1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = 2 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =

3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = 4 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =

3、 注意:(1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> aa≥0).(2)、只有a≥0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a才成立.

二、学生小组交流解疑,教师点拨、拓展

2 填空:当a≥0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_____;当a<0时, <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_______并根据这一性质回答下列问题.

1)若 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a,则a可以是什么数?

2)若 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =-a,则a可以是什么数?

3 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> >a,则a可以是什么数?

3x>2,化简 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> - <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>




三、巩固练习

教材练习

四、课堂检测

(一)、选择题

1 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值是( ). A0 B <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C4 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

(二)、填空题

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

2.若 <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是一个正整数,则正整数m的最小值是________

三、综合提高题

1.先化简再求值:当a=9时,求a+ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值,甲乙两人的解答如下:

甲的解答为:原式=a+ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a+1-a=1

乙的解答为:原式=a+ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a+a-1=2a-1=17

两种解答中,_______的解答是错误的,错误的原因是__________

2.若│1995-a│+ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =a,求a-19952的值.

(提示:先由a-2000≥0,判断1995-a的值是正数还是负数,去掉绝对值)

3. -3≤x≤2时,试化简│x-2│+ <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>