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:
[tex] \sqrt{27} = \sqrt{9*3} [/tex]
Now break up the 9 into its perfect square:
[tex] \sqrt{(3*3)*3} [/tex]
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
[tex]3 \sqrt{3} [/tex]
If you had the square root of 8, that would simplify to
[tex] \sqrt{8} = \sqrt{4*2} [/tex]
4 is a prfect square (2 times 2), so you can pull out a 2, leaving the other 2 under the radical
[tex] \sqrt{4*2} = \sqrt{(2*2)*2} =2 \sqrt{2} [/tex]
Hope that makes sense. If you'd like some more examples to help clarify, just ask!
