Simplify the following completely: .

This is a pretty basic rationalizing the denominator problem, so let's multiply by a fancy form of 1.

Next, we just have to simplify our factors. This is really no big deal.

Simplify the following completely: .

Again, we need to rationalize the denominator, so the first step doesn't change.

Our second step requires the multiplication of a couple square roots.

Last but not least, we need to simplify our fraction. Say goodbye to those 2s.

Simplify the following completely: .

There are a couple different ways to potentially attack this problem. We're going to choose to rationalize the denominator first.

It appears as though we can simplify the denominator pretty easily, so we'll head there next.

Finally, we need to simplify the √216. This is just a matter of applying our simple radical form technique. This means we need a product of primes. Or do we?

Before we get to our prime breakdown, we might notice that 216 is actually 6 × 6 × 6. This means we can pull a 6 out of the square root. This makes life so much easier.

Finally, we can simplify our fraction and move on.

Simplify the following completely: .

The first step here is to multiply our fractions. Remember to multiply across the numerator and denominator.

Next, we have a nice little fraction. This thing definitely needs to have its denominator rationalized. Do it.

This rationalization is great news for us since the √36 works out so well.

Last but not least, we'll simplify the fraction to get to our final answer. Score.