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# Simplifying square roots review

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:

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 $\sqrt{54{x}^{7}}$ 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.*

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