Cube root of a perfect cube

³√n

The trick, step by step

1. Look at the last digit: 175,616 ends in 6, and only 6³ = 216 ends in 6, so the root ends in 6.

   6

2. Drop the last three digits: 175. 5³ = 125 is the biggest cube not above 175, so the root starts with 5.

   1755

3. So ³√175,616 = 56.

   56

given working answer taken away

Why it works

Each last digit 0 to 9 gives a different last digit when cubed (2 and 8 swap, 3 and 7 swap, the rest stay), so the cube's last digit fixes the root's. Dropping three digits divides by 1000, and the root's tens digit is the biggest k with k³ not above what is left.