List of formulas relared to Roots functions
Notation:
a,b : bases (a≥0,b≥0 if n=2k)
n,m: powers
Formulas:
\[\left( \sqrt[\scriptstyle n]{a} \right)^n = a\]
\[\left( \sqrt[\scriptstyle n]{a} \right)^m = \sqrt[\scriptstyle n]{a^m}\]
\[\sqrt[\scriptstyle m]{ \sqrt[\scriptstyle n]{a}} = \sqrt[\scriptstyle {n m}]{a}\]
\[\left( \sqrt[\scriptstyle n]{a^m} \right)^p = \sqrt[\scriptstyle n]{a^{n p}}\]
\[\sqrt[\scriptstyle n]{a^m} = \sqrt[\scriptstyle n p]{a^{n p}}\]
\[\frac{1}{\sqrt[\scriptstyle n]{a}} = \frac{ \sqrt[\scriptstyle n]{a^{n-1}}}{a}\]
\[\sqrt[\scriptstyle n]{ab} = \sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle n]{b}\]
\[\sqrt[\scriptstyle n]{\frac{a}{b}} = \frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle n]{b}}\]
\[\frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle m]{b}} = \sqrt[\scriptstyle {nm}]{\frac{a^m}{b^n}}\]
\[\sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle m]{b} = \sqrt[\scriptstyle{nm}]{a^m b^n}\]
\[\sqrt{ a \pm \sqrt{b}} = \sqrt{ \frac{a + \sqrt{a^2 - b}}{2}} \pm \sqrt{ \frac{a - \sqrt{a^2 - b}}{2}}\]
\[\frac{1}{\sqrt{a} \pm \sqrt{b}} = \frac{\sqrt{a} \mp \sqrt{b}}{a-b}\]
