# Simplifying a Radical (Part 2)

How to simplify a radical (Part 2): examples and their solutions.

## Example 1

Factor 18: 2⋅3^{2}.

Divide each factor's power by 2 (square root).

Write the powers as (quotient)⋅2 + (remainder).

3^{2} = 3^{1⋅2}*x*^{4} = *x*^{2⋅2}*y*^{7} = *y*^{3⋅2 + 1}

Make square forms.

3^{1⋅2} = 3^{2}*x*^{2⋅2} = (*x*^{2})^{2}*y*^{3⋅2 + 1} = (*y*^{3})^{2}⋅*y*

Take the available base parts

out from the radical sign:

3, *x*^{2}, and *y*^{3}.

For *y*^{3}, add an absolute value sign: |*y*^{3}|*n*th root of a number

Simplifying a radical (part 1)

## Example 2

Factor 16: 2^{4}.

Divide each factor's power by 3 (cube root).

Write the powers as (quotient)⋅3 + (remainder).

2^{4} = 2^{1⋅3 + 1}*x*^{5} = *x*^{1⋅3 + 2}*y*^{9} = *y*^{3⋅3 + 0}

Make square forms.

2^{1⋅3 + 1} = 2^{3}⋅2*x*^{1⋅3 + 2} = *x*^{3}⋅*x*^{2}*y*^{3⋅3 + 0} = (*y*^{3})^{3}

Take the available base parts

out from the radical sign:

2, *x*, and *y*^{3}.*n*th root of a number