How to Calculate a Cube Root Using the Division Method

One of my viewers has asked me to produce a video showing how to calculate cube roots using the "division method." Thank you, Prashant. This video is for you.

In the firt part of the video I demonstrate the method that I prefer (there are "variations on the theme"). I then explain how the method works by discussing the binomial expansion of
(a + b)³ = a³ + 3a²b + 3ab² + b³.

If you have watched my earlier videos, you will see that the "theory" behind the method is essentially the same as that which lies behind the iterative method(s).

Because calculators are so readily available now, this skill is no longer used in any practical sense. Historically, it was one of the methods used to calculate roots for the mathematical tables that were used before mechanical calculators were easy to obtain.

The reason for my presenting it is to help better students gain insights into how algebra, graphing and calculus can help us understand how to manipulate numbers. So much theory of numbers is developed this way that this is a very worthwhile video for the serious mathematics student.

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