Chapter 3, Problem 1PP

(This is a version of Programming Project 2.1 from Chapter 2.) The Babylonian algorithm to compute the square root of a positive number n is as follows:

1. Make a guess at the answer (you can pick $\text{n/2}$ as your initial guess).

2. Compute $\text{r }=\text{ n}/\text{guess}\text{.}$

3. Set guess $=\left(\text{guess}+\text{r}\right)/2.$

4. Go back to step 2 until the last two guess values are within 1% of each other.

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.