Here's how you do cube roots in your head! Avoid looking like Education Secretary Nicky Morgan who was stumped when asked to do a cube root: https://www.youtube.com/watch?v=x8CV0dfQMdU
Note: the starting number needs to be a perfect cube. So it's more of a magic trick: ask someone to cube a number and then you can deduce their original number quickly.
Check out my book "The Best Mental Math Tricks" (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo
Can you multiply 97 by 96 in your head? Or can you figure out the day of the week when you are given a date? This book is a collection of methods that will help you solve math problems in your head and make you look like a genius. "The Best Mental Math Tricks" (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo
Arthur Benjamin is a Professor at Harvey Mudd College and well-known for feats of mental calculation. He explains the cube root algorithm in this pdf https://www.math.hmc.edu/~benjamin/papers/Cubing.pdf
This trick is really old--here's a newspaper article from 1913 that explains the trick! http://cdnc.ucr.edu/cgi-bin/cdnc?a=d&d=SFC191306126.96.36.199.11
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