# Cube root

In

mathematics, the

**cube root** of a number is a number which, when cubed (multiplied by itself and then multiplied by itself again), gives back the original number. For instance, the cube root of 8 is 2, because 2 × 2 × 2 = 8. This is written:

Formally, the cube root of a

real (or

complex) number

*x* is a real (correspondingly, complex) solution

*y* to the equation:

- y
^{3} = x,

which leads to the equivalent notation for cube and other roots that

A non-zero complex number has three cube roots. A real number has a unique real cube root, but when treated as a complex number it has two further cube roots, which are complex conjugates of each other.

For instance, the cube roots of unity are 1, (− 1 + √3*i*)/2 and (− 1 − √3*i*)/2 .

See also: