# Arithmetic Course/Number Operation/Root

## Root

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

## Rules

Square root of zero is

${\displaystyle {\sqrt {0}}=}$

Square root of one is one

${\displaystyle {\sqrt {1}}=1}$

Square root of negative one is an imaginary number j

${\displaystyle {\sqrt {-1}}=j}$

## Identities

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