Posted by **aymee** on Thursday, February 23, 2012 at 5:36am.

Ancient square root algorithm. The Babylonian algorithm to compute the square root of a number n is as follows:

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

2. Compute r = n / guess

3. Set guess = (guess + r) / 2

4. Go back to step 2 for as many iterations as necessary.

The more that steps 2 and 3 are repeated, the closer guess

will become to the square root of n.

Write a program that inputs an integer for n, iterates through the Babylonian algorithm until guess is within 1% of the previous guess, and outputs the answer as a double.

Input Details: The input will consist of a single integer. It is prompted for by the string "Enter number to compute the square root of."

Output Details: The program prints the label "The estimate of the square root of X is" followed by the estimate of the square root, where X is the number read in whose square root is being estimated. All numerical values should be printed with exactly two digits past the decimal point.

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