# Simplifying a Radical (Part 1)

How to simplify a radical (Part 1): examples and their solutions.

## Example 1

Make the factors of the radicand

in squared form:

2^{2}, *x*^{2}

Then the square root and the square are cancelled.

And the bases (2, *x*) can get out from the radical sign.

## Example 2

Make the factors of the radicand

in squared form:*a*^{2}, (*c*^{2})^{2}

Then the square root and the square are cancelled.

And the bases (*a*, *c*^{2}) can get out from the radical sign.

## Example 3

To make the squared form:

Change 12 to 2^{2}⋅3

(prime factorization)

Change *k*^{7} to *k*^{6}⋅*k*.

(make an even power: 6)

Make the factors of the radicand

in squared form:

2^{2}, (*k*^{3})^{2}

Then the square root and the square are cancelled.

And the bases (2, *k*^{3}) can get out from the radical sign.