Cube root

In mathematics, the cube root of a number is a number which, when cubed (multiplied by itself three times), gives back the original number. For instance, the cube root of 8 is 2, because 2 x 2 x 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:

y³ = x,

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

³√x = x^1/₃

A 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+√3i)/2 and (-1-√3i)/2 .

See also:

• Square root
• Root of unity