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 group: Find the square root of 152.2756. Find the cube root of 4192 to the nearest hundredth. The principal "n"th root of a positive number can be computed using logarithms. Starting from the equation that defines "r" as an "n"th root of "x", namely formula_80 with "x" positive and therefore its principal root "r" also positive, one takes logarithms of both sides (any base of the logarithm will do) to obtain The root "r" is recovered from this by taking the antilog: For the case in which "x" is negative and "n" is odd, there is one real root "r"