The result was that the square root function was more than two times faster than x ** .5. What this means is the algorithm is much faster for calculating the square root, than calculating a fractional power, which is pretty much a given.

Logically, I used the "inspect" module, and did inspect.getsource(math.sqrt). However, it yielded an error, and I couldn't find out how they did it.

So, I began looking at square root algorithms and I found a good one: Newton's Method of Approximation

What it does is it begins with an initial guess, and it finds the average between the guess and the number/ guess. It does that over and over again, iterating for 100 times, but usually arriving at the square root within 10 iterations. The code looks something like this: