How do you find the cubic root? - Answers

One way to find the square root of a number is an iterative method. This entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage. One such method is the Newton-Raphson method. To start with, if you want to find the cube root if k, define f(x) = x3 - k. Then finding the cube root of k is equivalent to solving f(x) = 0. Let f'(x) = 3x2. This is the derivative of f(x) but that is not important for simply using the N-R method. Start with x0 as the first guess. Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, … After a few iterations, xn will be very close to the required root.