How do you simplify the square root of 48

When you simplify the square root of a number, you are looking for factors of the number that are perfect squares that you can remove from under the radical.  For example sq root of 8... it's not a perfect square but factors of 8 include 2 x 4... 4 is a perfect square so we can take it out of the radical by taking it's square root.  Now you are left with 2* sq root of 2.

For sq root of 48

48 = 12 x 4 

12 = 3x4  so we can say 48 = 3x4x4

so... sq root 48 = sq root 3x4x4

we have two 4's under the radical.  Sq root x^2 = x    so sq root 4^2 is 4

Pull it out from the radical and we are left with 4 * sq root 3