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 real number is a positive real number, negative numbers do not have real square roots. However, for every negative real number there are two imaginary square roots. For example, the square roots of −25 are 5"i" and −5"i", where "i" represents a number whose square is . A cube root of a number "x" is a number "r" whose cube is "x": Every real number "x" has exactly one real cube root, written formula_4. For example, Every real number has two additional complex cube roots. Expressing the degree of an "n"th root in its exponent form, as in formula_37, makes