If the cube root of 1331 is 11 and the cube root of 1728 is 12, what is the cube root of 1442897?

(Do this one in your head - no writing or calculators allowed!)

If we make the assumption that 1442897 has an integral cube root, we can conclude it must be 113. From the information given, we can deduce that the answer must be between 110 and 120 since 110 cubed must be 1331000 and 120 cubed is 1728000. The only digit which cubed results in a final digit of 7 is 3, hence 113.