Newton's Square Root Algorithm

Computer Science: Concepts & Explorations
David Reed

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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