Find the square root of a number [Babylonian method ]

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Find the square root of a number [Babylonian method ]

The Babylonian method, also known as Heron’s, is an ancient iterative algorithm for finding a number’s square root. It dates back to ancient Babylon, around 1800 BC.

Babylonian Algorithm to Find Square Root:

Start with an Initial Guess

Choose an initial guess (estimate) for the square root of the number you’re interested in.

Let’s call this guess x

Iterate: Use the following formula to improve your guess:

Apply the Formula:

xnew = ( x + n/x)/2

Iterate and Repeat: Continue applying the formula until the value of

abs( xnew – x ) <= error tolerance

is sufficiently close to meaning that the guesses are converging to the true square root.

The Babylonian method is efficient and converges quickly, making it a practical approach for calculating square roots.

RAPTOR Flowchart

Babylonian method

RAPTOR Square Root Babylonian

Flowchart Output

teration : 1 , xnew = 80.6123
Iteration : 2 , xnew = 44.1827
Iteration : 3 , xnew = 29.1643
Iteration : 4 , xnew = 25.2973
Iteration : 5 , xnew = 25.0017
Iteration : 6 , xnew = 25.0000
Iteration : 7 , xnew = 25
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Square root of 625 = 25
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Babylonian Flowchart Output