How to calculate cube root by hand?

Answer 1

Better use a scientific calculator to do this. It is just too much work otherwise. Now, let's assume you simply want to know how to do it, for completeness sake.

One method is to use trial and error. Say you want the cubic root of 20. You calculate the cube of 2 (2 x 2 x 2), which is 8, and the cube of 3 (3 x 3 x 3) which is 27. You conclude that the cubic root of 20 must be more than 2, but less than 3. You continue trying other numbers, for example, 2.53, and get a better and better approximation.

There are other methods that have a faster convergence, that means that they approach the result quicker. Those methods are explained in detail in calculus courses. In any case, just like the trial and error method explained above, those methods are iterative - i.e., you have to repeat certain calculations over and over again, getting closer and closer to the final result. At some point you decide that you are close enough to the number you want.