Cube Roots

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:

  1. 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 (63) is the first cube less than 250 — giving us 6.
  2. 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 (33). This number is the last digit of the cube root.
  3. Voila! Those are the 2 digits of the cube root — 6 and 3 — giving us 63 as the cube root of 250,047.