Fórmulas Radiciação

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Radiciação

1. Definição

$\sqrt[n]{a^{m}}=b$

$ \sqrt[n]{a^{m}} $	$:$	radical
$ \sqrt{\hspace{0.8em}} $	$:$	sinal do radical
$ n $	$:$	índice
$ a^{m} $	$:$	radicando
$ a $	$:$	base do radicando
$ m $	$:$	expoente do radicando
$b $	$:$	raiz n-ésima de $a^{m}$

2. Propriedades

$\sqrt[n]{a^{\style{font-size:110%}{m}}}=\sqrt[n.p]{a^{m.p}}$

$\sqrt[n]{a^{\style{font-size:110%}{m}}}=\sqrt[\frac{n}{\style{font-size:120%; font-weight: bold; font-style: normal; font-family: arial;}{p}}]{a^{\frac{m}{p}}}$

$\sqrt[n]{a\ .b}=\sqrt[n]{a}\ .\sqrt[n]{b}$

$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[\style{font-size:120%; font-weight: bold; font-style: normal; font-family: arial;}{n}]{b}}$

$(\sqrt[n]{a})^{p}=\sqrt[n]{a^{p}}$

$\sqrt[n]{\sqrt[m]{a}}=\sqrt[n.m]{a}$

$\sqrt[n]{a^{n}}=a$

3. Outras fórmulas

$0^{\frac{m}{n}} =0 \qquad$ se $\genfrac{}{}{1pt}{}{m}{n}>0$

$a^{\frac{m}{n}} =\sqrt[n]{a^{\style{font-size:120%; font-weight: bold; font-style: normal; font-family: arial;}{m}}}$

$\sqrt[n]{a} . \sqrt[m]{b} =\sqrt[n.m]{a^{m}.b^{n}}$

$\frac{\sqrt[n]{a}}{\sqrt[\style{font-size:120%; font-weight: bold; font-style: normal; font-family: arial;}{m}]{b}} = \sqrt[n.m]{\frac{a^{m}}{b^{\style{font-size:120%; font-weight: bold; font-style: normal; font-family: arial;}{n}}}} \qquad$ $(b \neq 0)$

$b^{n} = a \quad \rightarrow \quad b = \pm \sqrt[n]{a} \qquad$ para $a>0$ e $n$ par

$b^{n} = a \quad \rightarrow \quad b = \sqrt[n]{a} \qquad$ para $a \neq 0$ e $n$ ímpar