It is possible to write a funtion that will find a square root in a reasonable amount of time. The catch is that you'll have to use Calculus to do it. It's called Newton's Method. Newton's Method is used to approximate the zeroes of a function. In the case of finding a square root, you'd want to find the positive zero of a quadratic function.
f(x) = x^2 - num
where num is the number that you want to find the square root of. I know there's a coded solution to this in my textbook, but you should look it up yourself. To use Newton's Method you basically have to keep guessing at the zero until you get closer and closer to it. It's pretty fast and reasonably easy to code. You can also set up the calculations to continue untill a certain level of precision is reached. So, go google Newton's Method for approximately zeroes. Good luck!