Cube root can be done with a compass-and-straightedge construction. Newton's method is an iterative method that can be used to calculate the cube root. For real floating-point numbers this method reduces to the following iterative algorithm to produce successively better approximations of the cube root of "a": The method is simply averaging three factors chosen such that at each iteration. Halley's method improves upon this with an algorithm that converges more quickly with each step, albeit consuming more multiplication operations: With either method a poor initial approximation of "x" can give very poor algorithm performance, and coming up with a good initial
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.