Nth root Nth root In mathematics, an "n"th root of a number "x", where "n" is usually assumed to be a positive integer, is a number "r" which, when raised to the power "n" yields "x": where "n" is the "degree" of the root. A root of degree 2 is called a "square root" and a root of degree 3, a "cube root". Roots of higher degree are referred by using ordinal numbers, as in "fourth root", "twentieth root", etc. For example: Any non-zero number, considered as complex number, has "n" different "complex roots of degree "n"" ("n"th roots), including those with
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