Cube root this required the construction, now known to be impossible, of the length . A method for extracting cube roots appears in "The Nine Chapters on the Mathematical Art", a Chinese mathematical text compiled around the 2nd century BCE and commented on by Liu Hui in the 3rd century CE. The Greek mathematician Hero of Alexandria devised a method for calculating cube roots in the 1st century CE. His formula is again mentioned by Eutokios in a commentary on Archimedes. In 499 CE Aryabhata, a mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave a method for finding
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