Square root of 5 one, when traversing the cube "surface" (the shortest distance when traversing through the "inside" of the cube corresponds to the length of the cube diagonal, which is the square root of three times the edge). The number can be algebraically and geometrically related to and , as it is the length of the hypotenuse of a right triangle with catheti measuring and (again, the Pythagorean theorem proves this). Right triangles of such proportions can be found inside a cube: the sides of any triangle defined by the centre point of a cube, one of its vertices, and the middle point
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"