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Finding square root of a number by Babylonian method

The Babylonian method for finding square roots involves dividing and averaging, over and over, to obtain a more accurate solution with each repeat of the process.
Inorder to find the square root of a number you need to follow the following steps.
  1. Make an initial guess for the square root 
  2. Divide the original number by this guess
  3. Find out the mean of the 2 numbers
  4. check if the difference between guess and quotient is less than the error if not then repeat the process again.
  5. use this mean value as your next guess
Let us take an example of finding out the square root of 7 to 3 decimal places

let n = 7 and error = 0.001
let us take an initial guess = 3

Step 1: Guess = 3 
Step 2: Divide 7 by 3 = 2.3333333
Step 3: Find average of 3 and 2.333333 = 2.666666 (because (2+2.333333)/2 = 2.666666)
Step 4: difference (3 - 2.3333333) > error hence repeat the process again
Step 5: Next guess is 2.666666

Step 1: Guess 2.666666
Step 2: Divide 7 by 2.666666 = 2.624999 
Step 3: Find average of 2.666666 and 2.624999 = 2.645832
Step 4: difference (2.666666 - 2.624999) > error hence repeat the process again
Step 5: Next guess is 2.645832

Step 1: Guess 2.645832
Step 2: Divide 7 by 2.645832 = 2.645670
Step 3: Find average of 2.645832 and 2.645670 = 2.645751
Step 4: difference (2.645832 - 2.645670) < error hence stop and print the answer
Step 4: FINAL guess is 2.645751

Now CHECK your final guess with a calculator: sqrt 7 = 2.645751

C Program

C++ Program

Sample input and output to check the program


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