Newton's method to approximate the square root of a number n is the following. First, make an initial guess x0. Then compute x1 = 1 /2 (x0 + n/x0), and keep using this formula to generate a sequence x0, x1, x2, x3....

(a) Convince yourself numerically that the sequence converges to the square root of n by testing this procedure for a few values of n and various initial guesses.

(b) make a program that prompts the user for a positive number n and produces its square root using Newton's method. (Question: Which criteria do you use for stopping the algorithm?)