All Maths Formulas

Algebra

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

$n , m$ : powers

(a \sqrt n) n = a

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

(a \sqrt n) m = a m - - - \sqrt n

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

a \sqrt n - - - \sqrt m = a \sqrt n m

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

(a m - - - \sqrt n) p = a n p - - - \sqrt n

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

a m - - - \sqrt n = a n p - - - \sqrt n p

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

1 a \sqrt n = a n - 1 - - - - \sqrt n a

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

a b - - \sqrt n = a \sqrt n \cdot b \sqrt n

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

a b - - \sqrt n = a \sqrt n b \sqrt n

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

a \sqrt n b \sqrt m = a m b n - - - \sqrt n m

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

a \sqrt n \cdot b \sqrt m = a m b n - - - - \sqrt n m

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

a \pm b \sqrt - - - - - - \sqrt = a + a 2 - b - - - - - \sqrt 2 - - - - - - - - - - \sqrt \pm a - a 2 - b - - - - - \sqrt 2 - - - - - - - - - - \sqrt

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

1 a \sqrt \pm b \sqrt = a \sqrt \mp b \sqrt a - b

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

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