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
Root-finding algorithm cubic polynomial may involve non-real cube roots). For polynomials of degree five or higher Abel–Ruffini theorem asserts that there is, in general, no radical expression of the roots. So, except for very low degrees, root finding of polynomials consists of finding approximations of the roots. By the fundamental theorem of algebra, one knows that a polynomial of degree has at most real or complex roots, and the this number is reached for almost all polynomials. It follows that the problem of root finding for polynomials may be split in three different subproblems; For finding one root, Newton's method and other