How do you simplify the square root of 27?

Start by finding the numbers that go into 27.  1, 27...3, 9...I think that's it, right? One of those numbers is a perfect square.  The 9.  Rewrite the radical like this then:

Now break up the 9 into its perfect square:

Because there are 3 3's you can pull out the root of 9, which is one of those 3's.  It will then simplify to

If you had the square root of 8, that would simplify to

4 is a prfect square (2 times 2), so you can pull out a 2, leaving the other 2 under the radical

Hope that makes sense. If you'd like some more examples to help clarify, just ask!