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:
- <math>\sqrt[3]{8} = 2<math>
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
- <math>y = x^{1\over3}<math>
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 + √3i)/2 and (− 1 − √3i)/2 .
See also
