Conversation so far:
what is the method of finding square root
The most familiar such method, most suited for programmatic calculation, is Newton's method, which is based on a property of the derivative in the calculus.
what is used to find calculations of square root
The methods may be those suitable for mental calculation, requiring at least paper and pencil, and those which are implemented as programs to be executed on a digital electronic computer.

Question: since when have the methods been known
Self-contained rewrite: since when have the methods of calculating square roots been known