wPrime uses a recursive call of Newton's method for estimating functions, with f(x)=x2-k, where k is the number we're sqrting, until Sgn(f(x)/f'(x)) does not equal that of the previous iteration, starting with an estimation of k/2. It then uses an iterative calling of the estimation method a set amount of times to increase the accuracy of the results. It then confirms that n(k)2=k to ensure the calculation was correct. It repeats this for all numbers from 1 to the requested maximum.
Coming off the games, you can see the massive boost in performance when it comes down to CPU performance. That extra 1GHz+ does wonders for performance.