Doubling the cube given length times . In music theory, a natural analogue of doubling is the octave (a musical interval caused by doubling the frequency of a tone), and a natural analogue of a cube is three repetitions of the same interval. In this sense, the problem of doubling the cube is solved by the major third in equal temperament. This is a musical interval that is exactly one third of an octave. It multiplies the frequency of a tone by , the side length of the Delian cube. Doubling the cube Doubling the cube, also known as the Delian problem, is
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"