Chapter 2, Problem 9PP

(This is an extension of an exercise from Chapter 1.) The Babylonian algorithm to compute the square root of a positive number n is as follows: $n/2$

1. Make a guess at the answer (you can pick as your initial guess).
2. Compute $r=n/\text{guess}\text{.}$
3. Set $\text{guess}=\left(\text{guess}+r\right)/2.$
4. Go back to step 2 for as many iterations as necessary. The more steps 2 and 3 are repeated, the closer guess will become to the square root of n.

Write a program that inputs a double for n, iterates through the Babylonian algorithm until the guess is within $1\%$ of the previous guess, and outputs the answer as a double to two decimal places. Your answer should be accurate even for large values of n.