How does a calculator find a square root? One of the oldest and fastest ways starts with any guess and keeps improving it: take the average of the guess and the number divided by the guess. This is Newton's method, and on a graph every step is a tangent line sliding down to the axis. Try it on your own numbers and watch the number of correct digits roughly double with every step.
This article and its interactive demo were created with the help of generative AI and editorially reviewed.