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