Cube root

In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of 8 are and . The three cube roots of −27i are:


In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the principal cube root, denoted with the radical sign The cube root is the inverse function of the cube function if considering only real numbers, but not if considering also complex numbers: although one has always the cube of a nonzero number has more than one complex cube root and its principal cube root may not be the number that was cubed. For example, , but

Plot of y = 3x. The plot is symmetric with respect to origin, as it is an odd function. At x = 0 this graph has a vertical tangent.
A unit cube (side = 1) and a cube with twice the volume (side = 32 = 1.2599... OEISA002580).