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:

`√(27) = √(9*3)`
Now break up the 9 into its perfect square:

`√((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 √(3)`
If you had the square root of 8, that would simplify to

`√(8) = √(4*2)`
4 is a prfect square (2 times 2), so you can pull out a 2, leaving the other 2 under the radical

`√(4*2) = √((2*2)*2) =2 √(2)`
Hope that makes sense. If you'd like some more examples to help clarify, just ask!