Cube root Cube root In mathematics, a cube root of a number "x" is a number "y" such that "y" = "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 , is 2, because 2 = 8, while the other cube roots of 8 are −1 + "i" and −1 − "i". The three cube roots of −27"i" are The cube root operation is not distributive with addition or subtraction. In
Doubling the cube at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, . This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible