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. Finally, if "x" is not real, then none of its "n"th roots is real. Roots are usually written using the radical symbol or "radix" with formula_2 denoting the principal square root of formula_3, formula_4 denoting the principal cube root, formula_5 denoting the principal fourth root, and so on. In the expression formula_6, "n" is called the "index", formula_7 is the "radical sign" or "radix", and formula_3 is called the "radicand". Since the radical symbol denotes a function, it is defined to return only one result for a given argument formula_3, which is called the principal "n"th root of formula_3.