Methods of computing square roots

There are many such methods. Since often square roots of even rational numbers are irrational, we need to know how precise the result is expected to be.

If the result does not have to very precise, the following approach could be helpful. Suppose you need to find square root of some number N. Find some number A such that A^2 (that is A times A) is approximately equal to N (but how close? This needs to be expanded). Then we can think of A as being approximately the square root of N.