Cube root (original) (raw)

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:

y3 = 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 .