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Cube root

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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 .

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This page was last modified 15:18, 26 May 2004.
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