Now that you know how to simplify square roots of integers that aren't perfect squares, we need to take this a step further, and learn how to do it if the expression we're taking the square root of has variables in it. Don't panic! It might sound hard, but it's actually easier than what you were doing in the previous section. (Honest!)

You see, in the previous section, you began by doing a prime factorization. But if you're dealing with variables, you get to skip that step - it's already done for you!

Here's an example: Simplify

From the previous section, we know what to do with this. We rewrite x⁹ as a product which contains a perfect square:

x⁹ = x⁸ · x¹

= =  · = x⁴

That wasn't so bad, was it?

Let's try another. This time we'll include multiple variables. Simplify

The exponents that are bigger than 2, and odd, we need to rewrite.

=
= 
 · = 
x⁴y³z²

That wasn't so hard, was it?

Of course, I could make it a bit more difficult, by including a number with the variables: Simplify .

In this case we need to do a factorization of 12, and then rewrite the expression using that facttorization:

= =  · = 2x²y

1.

Simplify

2.

Simplify

3.

Simplify

4.

Simplify

5.

Simplify