A number that, when multiplied by itself, gives the original number. The square root of 16 is 4 because 4 × 4 = 16, written as √16 = 4.
Combines 'square' (referring to the geometric shape and the operation of squaring) with 'root' (from Latin 'radix' meaning source or origin). Ancient civilizations knew square roots geometrically through the diagonal of squares, but the radical symbol √ was introduced in 1525 by Christoff Rudolff.
Square roots connect geometry and algebra in beautiful ways - they represent the side length of a square with a given area! The ancient Babylonians could approximate square roots to remarkable accuracy 4,000 years ago, and the discovery that √2 is irrational (can't be expressed as a fraction) shocked the ancient Greeks and helped birth modern mathematics.
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