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