# Simplifying square roots review

CCSS Math: HSN.RN.A.2

Learn how to rewrite square roots (and expressions containing them) so there's no perfect square within the square root. For example, rewrite √75 as 5⋅√3.

## Simplifying square roots

### Example

Let's simplify $\sqrt{75}$ by removing all perfect squares from inside the square root.

We start by factoring $75$, looking for a perfect square:

$75=5\times5\times3=\blueD{5^2}\times3$.

We found one! This allows us to simplify the radical:

So $\sqrt{75}=5\sqrt{3}$.

*Want another example like this? Check out this video.*

## Simplifying square roots with variables

### Example

Let's simplify $\sqrt{54x^7}$ by removing all perfect squares from inside the square root.

First, we factor $54$:

Then, we find the greatest perfect square in $x^7$:

And now we can simplify:

## More challenging square root expressions

*Want to try more problems like these? Check out this exercise.*