Simplifying radicals in my trigonometry.

I am having a problem coming up with the correct solutions to work. The reason being I don't really understand how to work with radicals.

A simple example of my problem is this.

sqrt(33) * sqrt(32)

I know the answer is 4sqrt(66) but I have no idea why.

Another example of an answer I got in my problem that I cannot simplify is here (-4/-sqrt(33) + -sqrt(32)/2) /( 1 + -4/sqrt(33) + -sqrt(32)/2 ) - Wolfram|Alpha. (sorry for the link wolfram's makes it look pretty)

I think I may have messed up some of the positives and negatives.

I am using the sum formula for tangent.

Tana = -4/-sqrt(33)

Tanb = -sqrt(32)/2

Can anybody point me in the direction of a radical tutorial somewhere or give me some pointers?

Thanks!