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
Cube root or the other of the two complex cube roots of 1. For complex numbers, the principal cube root is usually defined as the cube root that has the greatest real part, or, equivalently, the cube root whose argument has the least absolute value. It is related to the principal value of the natural logarithm by the formula If we write "x" as where "r" is a non-negative real number and "θ" lies in the range then the principal complex cube root is This means that in polar coordinates, we are taking the cube root of the radius and dividing the