Question

How do you simplify the square root of 27?

Answer 1

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