Newton's Square Root Algorithm

Visualization Tool to Accompany
A Balanced Introduction to Computer Science, 3rd ed.
David Reed, Prentice Hall, © 2010.

In order to approximate the square root of some number N, Newton's algorithm starts with an initial approximation of 1, then repeatedly refines the approximation by averaging the old approximation with N over the old approximation. More succinctly,

newApproximation = (oldApproximation + N/oldApproximation)/2

To see Newton's algorithm in action, enter the number for which you want to compute the square root, then click the button to see each successive approximation.

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