初中数学公式之二次根式公式

初中数学公式 — 二次根式

一、二次根式的概念

形如 $\sqrt{a}$（$a \geq 0$）的式子叫做二次根式。$\sqrt{a} \geq 0$（$a \geq 0$）具有双重非负性。

二、最简二次根式

满足以下两个条件的二次根式：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。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

如：$\sqrt{12} = 2\sqrt{3}$，$\sqrt{\dfrac{1}{3}} = \dfrac{\sqrt{3}}{3}$文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

三、二次根式的运算

乘法：$\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$（$a \geq 0$，$b \geq 0$）文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

除法：$\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$（$a \geq 0$，$b > 0$）文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

加减：先化简为最简二次根式，再合并同类二次根式。$m\sqrt{a} \pm n\sqrt{a} = (m \pm n)\sqrt{a}$文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

分母有理化：$\dfrac{1}{\sqrt{a}} = \dfrac{\sqrt{a}}{a}$；$\dfrac{1}{\sqrt{a}+\sqrt{b}} = \dfrac{\sqrt{a}-\sqrt{b}}{a-b}$文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html

文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html 文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhiercigenshigongshi.html