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 zero

$\sqrt{0}=0$

Square root of one is one

$\sqrt{1}=1$

Square root of negative one is an imaginary number i

$\sqrt{-1}=i$

Identities

1. $\sqrt{a}\sqrt{-a}=\sqrt{-a^2}=i\sqrt{a^2}$
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. $(\sqrt{a}{)}^n=a^{(}n-2)$