Henry Ernest Dudeney/Modern Puzzles/69 - Root Extraction

by : $69$

 * Root Extraction
 * In a conversation I had with Professor Simon Greathead, the eminent mathematician, ...
 * the extraction of the cube root.
 * "Ah," said the professor, "it is astounding what ignorance prevails ...
 * ... the simple fact that, to extract the cube root of a number, all you have to do is to add together the digits.
 * Thus, ignoring the obvious case of the number $1$, if we want the cube root of $512$, add the digits -- $8$, and there you are!"
 * I suggested that that was a special case.
 * "Not at all," he replied. "Take another number at random -- $4913$ -- and the digits add to $17$, the cube of which is $4913$."
 * I did not presume to argue ... all the other numbers whose cube root is the same as the sum of their digits.


 * They are so few that they can be counted on the fingers of one hand.