توجه:

a و b: پایه  \(( a \geq 0 , b \geq 0 ~~\text{if} ~~ n = 2k )\)

n و m: توان

فرمول ها:

\(\left( \sqrt[\scriptstyle n]{a} \right)^n = a\)

\(\left( \sqrt[\scriptstyle n]{a} \right)^m = \sqrt[\scriptstyle n]{a^m}\)

\(\sqrt[\scriptstyle m]{ \sqrt[\scriptstyle n]{a}} = \sqrt[\scriptstyle {n m}]{a}\)

\(\left( \sqrt[\scriptstyle n]{a^m} \right)^p = \sqrt[\scriptstyle n]{a^{m p}}\)

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

\(\frac{1}{\sqrt[\scriptstyle n]{a}} = \frac{ \sqrt[\scriptstyle n]{a^{n-1}}}{a}\)

\(\sqrt[\scriptstyle n]{ab} = \sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle n]{b}\)

\(\sqrt[\scriptstyle n]{\frac{a}{b}} = \frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle n]{b}}\)

\(\frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle m]{b}} = \sqrt[\scriptstyle {nm}]{\frac{a^m}{b^n}}\)

\(\sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle m]{b} = \sqrt[\scriptstyle{nm}]{a^m b^n}\)

\(\sqrt{ a \pm \sqrt{b}} = \sqrt{ \frac{a + \sqrt{a^2 - b}}{2}} \pm \sqrt{ \frac{a - \sqrt{a^2 - b}}{2}}\)

\(\frac{1}{\sqrt{a} \pm \sqrt{b}} = \frac{\sqrt{a} \mp \sqrt{b}}{a-b}\)