Square Root Calculator

The square root of a number x is the number that gives x when multiplied by itself. It is written √x, so √49 = 7 because 7 × 7 = 49. Every positive number has two square roots, one positive and one negative (7 and −7); the √ sign means the positive one.

Square roots turn up whenever an area has to become a length: a square room of 400 sq ft is √400 = 20 ft on each side, and a 36 m² plot is 6 m square. They are also at the heart of the Pythagorean theorem, c = √(a² + b²), so a 3 by 4 rectangle has a diagonal of √25 = 5.

A cube root is the number that gives x when used three times: ∛27 = 3 and ∛1000 = 10. The calculator shows the cube root under every square root. In general, the nth root of x is x^1/n; the fourth root of 81 is 3 because 3⁴ = 81.

Even roots (square, fourth …) of negative numbers are not real, but odd roots are: ∛−125 = −5. For negative inputs the calculator gives the square root in terms of the imaginary unit i, as in √−9 = 3i.