# Indices law - law 3

## `a^(1/n)=\rootna`

To remember this try simple numbers you know first.

We know `4^(1/2)=sqrt4=2`

We can then apply this to all other examples:

**Example 1 **

`10\^(1/2)=\root2\10=3.162`

**Example 2 **

`9\^(1/2)=\root2\9=3` `(3xx3 =9)`

The second root of `9=3`

(The second root is also known as the square root)

**Example 3 **

`27\^(1/3)=\root3\27=3` `(3xx3xx3=27)`

The third root of `27=3`

(The third root is also known as the cube root)