If you are not able to use a calculator to find the square root of a number, and you do not know it, you can use a method called splitting factors. In this method you take out the smallest number of factors you can until a number is just a list of factors. For an example, we'll work with 144.
144 ----> take out a factor of 2.
(2)(72) -----> you can take out another 2
(2)(2)(36) ----> and another
(2)(2)(2)(18) ---> and another
(2)(2)(2)(2)(9) -----> Now we can't take a 2, but we can take a 3
(2)(2)(2)(2)(3)(3)
At this point, we have only prime numbers. Once you get to this step, you need to group them into groups of 2. You can only do this if they are the same number. So we have a group of 2s, another group of 2s and a group of 3s.
2-2, 2-2, and 3-3
For the last step, you eliminate one of each of the group and multiply them all together.
2*2*3 = 12
And the square root of 144 is 12. Many teachers will have you try to memorize all the square roots up to a certain number, but if you ever don't know, this works all the time.
