Newton's Method

Here is a review of the method:

To compute the square root of N make a first guess, then improve that guess using the formula:

newGuess = N/(2*oldGuess) + oldGuess/2

For example, say that you want the square root of N = 3.00. Let's use 1 for the first guess. The new guess is

newGuess = 3/(2*1) + 1/2 = 3/2 + 1/2 = 2.0

Now this guess is improved by using it as the oldGuess in the formula.

The improved guess just computed, 2.0, now plays the role of oldGuess:

newGuess = 3/(2*2.0) + 2.0/2 = 3/4 + 1.0 = 1.75

Another round further improves the guess:

newGuess = 3/(2*1.75) + 1.75/2 = 3/3.5 + 1.75/2 
         = 0.85714.. + 0.87500 = 1.73214..