Cube (algebra) however, easy to show that most numbers are not perfect cubes because "all" perfect cubes must have digital root 1, 8 or 9. That is their values modulo 9 may be only −1, 1 and 0. Moreover, the digital root of any number's cube can be determined by the remainder the number gives when divided by 3: Every positive integer can be written as the sum of nine (or fewer) positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine positive cubes: The equation has
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