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【329886】9.1 二次根式和它的性质

时间:2025-02-07 09:22:32 作者: 字数:2537字



9.1二次根式和它的性质


【学习目标】

  1. 理解二次根式的概念,会判断一个式子是否为二次根式,明确被开方数必须是非负数,能找出使二次根式有意义的条件,会判断二次根式是否有意义。

  2. 理解最简二次根式的概念,会运用积的算术平方根的性质和商的算术平方根的性质将二次根式化简。

知识准备

算术平方根:_____________________________________________

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 = a (a <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ) 注意:负数没有算术平方根。

自学提示

预习课本第112—117页的内容,完成以下知识:

  1. 二次根式:__________________________________________其中a叫做____________.

  2. 二次根式的性质

1 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,即一个非负数的算术平方根是一个________________

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 = <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ),即一个二次根式的平方等于它的_________________

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 = <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =_______________即任意一个数的平方的算术平方根等于它本身的绝对值。

2)积的算术平方根,等于______________________________________________

符号表示:_______________________________________

3)商的算术平方根,等于_______________________________________________

符号表示:________________________________________

  1. 最简二次根式:___________________________________________________________-

问题积累

我的学习困惑是:____________________________________________________________-

共同释疑

1. 1 x取什么实收时,二次根式 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 在实数范围内有意义?


对应练习 当 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 取什么实数时,下列各式有意义?

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


2计算:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 ; (— <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 ; (—3 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

对应练习

计算: ( <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 ; (— <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>2 2 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 ; (—5 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

3 化简:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>



对应练习 化简:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>



4 把下列各式化成最简二次根式:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>



对应练习

把下列各式化成最简二次根式:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


当堂测试

1. <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 取什么实数时,下列各式有意义?

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2.化简:

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

  1.  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,则 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的取值范围是_________________

  2. (选做题)已知—2 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,化简 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>