Methods of computing square roots

There are a numbers of ways to calculate the square root of a number, and even more ways to estimate it.

Firstly, one needs to know how precise the result is expected to be. This is because often square roots are irrational. For example, square root of nice round number 2 is a fraction which in its decimal notation has infinite length, and therefore it is impossible to express it exactly.

Moreover, for some real numbers the square root is a complex number. For example, square root of -4 is a complex number 2i.

Also, please keep in mind that in some situations there may be multiple valid answers. For example, square root of 4 is 2, but also -2. You can verify that they are both valid answers by squaring each candidate answer and checking if you obtain 4 as the result of verification.

If the result does not have to be very precise, the following approaches could be helpful:

Methodology	Example of Usage
Suppose you need to find square root of some number N. Find some number A such that $A^{2}$ (that is A squared, or 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.	Suppose we need to estimate the square root of 71. We know that 8 squared is 64, and 9 squared is 81. Therefore, square root of 71 is somewhere between 8 and 9.