Newton's Method for Calculating a Square Root

This method involves a bit of multiplying and dividing but it will arrive at the precise square root over time and trials:

Step 1) Let X be the number of which you wish to find the square root. Let G be your best guess at each stage of the calculation.
Step 2) To find the next G, call it G', you set G' equal to:

G' = ( X + G^2) / 2G

Step 3) This G' becomes your next G. Iterate, that is repeat the calculation over and over (as shown below), and you will eventually arrive at the square root you seek.

G'' = ( X + G'^2) / 2G'

G''' = ( X + G''^2) / 2G''