Arithmetic Course/Number Operation/Root

Root

Root is an arithmatic operation opposite to power . If there exists $a ^ n = b$ Then $\sqrt{b} = a$

Rules

Square root of zero is

$\sqrt{0} =$

Square root of one is one

$\sqrt{1} = 1$

Square root of negative one is an imaginary number j

$\sqrt{-1} = j$

Identities

1. $\sqrt{a} \sqrt{-a} = \sqrt{-a^2} = j \sqrt{a^2}$
2. $\sqrt{a} \sqrt{a} = a$
3. $\sqrt{a} \sqrt{b} = \sqrt{ab}$
4. $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$
5. $\sqrt{a^n} = a \sqrt{a^(n-2)}$
6. $(\sqrt{a})^n = a ^(n-2)$