How could I be able to find a square root without first squaring a certain number that equals the number I want to square? I am very confused on this topic and would like to know a lot more about it.
You could use an iterative numerical method. Suppose you want to find the square root of the number m, say.
Makle an initial guess x0 (just set it to m/4 or something like it) then for a number of iterations i, use
xi = (xi-1 + m/xi-1)/2 until xi is the same as xi-1.
For example, suppose you want to find the square root of 3: