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,

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.