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
A boat travels 45 miles east then 60 miles north, how far is it from where it started. Draw this. The hypotenuse of the right triangle is the square root (45^2)+(60^2)=square root of 2025=3600=square root of 5625, or 75 miles.
