This riveted me; I love mental maths. To cube root a number (assuming it’s a perfect cube), here are the steps, using 250,047 as our protagonist cube:

- Ignoring the last 3 digits of the cube, find the first cube which is less than the remaining digits. 250 (ignoring 047) is the number in question, and 216 (6
^{3}) is the first cube less than 250 — giving us 6. - Find the number from 1-10 that, when cubed, ends in the last digit of your cube. 250,047 ends in 7, which corresponds to the last digit of 27 (3
^{3}). This number is the last digit of the cube root. - Voila! Those are the 2 digits of the cube root — 6 and 3 — giving us 63 as the cube root of 250,047.

*Awesome.*