I have done some research and I will probably study the Newton method and Taylor series. Turns out these two methods are being used in many approximation algorithms and real-time applications, including the one I mentioned. https://en.wikipedia.org/wiki/Methods_of_computing_square_roots https://en.wikipedia.org/wiki/Division_algorithm
I am originally interested in algorithms for stepper motors. If you are so, I found two books used as references: https://www.amazon.com/dp/0198593856/ https://www.amazon.com/dp/085296417X/
I will also take a look at Numerical Recipes mentioned below. Thanks