How to Approximate the nth Root of Any Number

If you are a student who is interested in becoming a well rounded mathematician I believe you should, at least once, calculate the root of a number by hand. You will also benefit from understanding the principles involved. In this way you will see how the principles of algebra can help us understand and manipulate numbers better ... and that is always a worthwhile thing!

You will also be treading in the footsteps of mathematicians in history who had to make their calculations using techniques like these because they did not have access to electronic or mechanical calculators.

In this video I explain the principles for approximating a fifth root and generalise them to any root. I then calculate an approximation to the fifth root of 67 by hand. Try this out for yourself.

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