初中数学公式 — 实数
一、平方根与算术平方根
若 $x^2 = a$，则 $x$ 叫做 $a$ 的平方根。正数 $a$ 的平方根有两个：$\pm\sqrt{a}$
正数 $a$ 的正平方根 $\sqrt{a}$ 叫做 $a$ 的算术平方根。$0$ 的算术平方根是 $0$。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
负数没有平方根。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
二、立方根
若 $x^3 = a$，则 $x$ 叫做 $a$ 的立方根，记作 $\sqrt[3]{a}$。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
正数的立方根是正数，负数的立方根是负数，$0$ 的立方根是 $0$。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
三、实数分类
$\text{实数}\begin{cases}\text{有理数}\begin{cases}\text{整数}\begin{cases}\text{正整数}\\0\\\text{负整数}\end{cases}\\\\text{分数}\begin{cases}\text{正分数}\\\\text{负分数}\end{cases}\end{cases}\\\\text{无理数}\begin{cases}\text{正无理数}\\\\text{负无理数}\end{cases}\end{cases}$文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
四、实数的运算
实数范围内的运算律与有理数相同。有理数的运算法则和运算律在实数范围内仍然适用。文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
$\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$（$a \geq 0$，$b \geq 0$）文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
$\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$（$a \geq 0$，$b \gt 0$）文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html 文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html文章源自公式库网-https://www.gongshiku.com/html/201808/chuzhongshuxuegongshizhishishugongshi.html
