Chapter 2, Problem 1PP

The Babylonian algorithm to compute the square root of a positive number « is as follows:

1. Make a guess at the answer (you can pick n/2 as your initial guess).

$\begin{array}{l}\text{2}\text{. Computer}=n/\text{guess}\hfill \\ \text{3}\text{. Set guess}=\left(\text{guess}+r\right)/2\hfill \end{array}$

4. Go back to step 2 for as many iterations as necessary. The more you repeat steps 2 and 3, 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 five times, and outputs the answer as a double to two decimal places. Your answer will be most accurate for small values of n.