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cube root : ウィキペディア英語版
cube root

In mathematics, a cube root of a number ''x'' is a number ''a'' such that ''a''3 = ''x''. All real numbers (except zero) have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted \sqrt(), is 2, because 23 = 8, while the other cube roots of 8 are -1+\sqrti and -1-\sqrti. The three cube roots of −27''i'' are
:3i, \quad \frac-\fraci, \quad \text \quad -\frac-\fraci.
The cube root operation is not associative or distributive with addition or subtraction.
In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the ''principal cube root'', denoted with the radical sign \sqrt(). The cube root operation is associative with exponentiation and distributive with multiplication and division if considering only real numbers, but not always if considering complex numbers: for example, the cube of any cube root of 8 is 8, but the three cube roots of 8^3 are 8, \, -4+4i\sqrt , \, \text -4-4i\sqrt.
==Formal definition==
The cube roots of a number ''x'' are the numbers ''y'' which satisfy the equation
:y^3 = x.\

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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