## Radicals

For positive integer n and real number a, any real number x such that x

^{n}= a is called an n

^{th}root of a.

- For n
= 2, an n
^{th}root is called a square root

- For n
= 3, an n
^{th}root is called a cube root

- The principal n
^{th}root of a, which is the positive n^{th}root of a is denoted by

- The principal n
^{th}root of 0 equals zero:

- If a < 0, the principal n
^{th}root of a, is defined as a real number only when n is odd

Terminology:

The symbol is referred to as the radical sign (or radical) while the positive integer n is called the index and real number a under the radical is the radicand.

Considering:

Properties of Radicals:

It follows that:

index = 3,

radicand = 125,

principal 3

radicand = 125,

principal 3

^{rd}root of radicand = 5Properties of Radicals: