Square Roots on the Number Line – Construction and Approximation

MathematicsNumbers & ArithmeticAges 12–13

Construct √2 as the diagonal of a unit square, then chain right triangles with leg 1 to build √3, √4, … √n (the Theodorus spiral), and swing an arc to mark that length on the number line. Below, a zoomed number line shows each decimal digit: drag the test point x to compare x² with n, then click 'Add a digit' to squeeze √n ever tighter and see why √n is irrational when n is not a perfect square.