You are told that 1,331 is a perfect cube. Can you guess without factorisation is its cube root? Similarly, guess the cube roots of 4913,12167,32768

Solution:

1331:

It lies between $10^3$ = 1000 and $20^3$ = 8000 and it’s last digit is 1. Cube of 1 is 1

cube root of 1331 = 11

4913:

It lies between $10^3$ = 1000 and $20^3$ = 8000 and it’s last digit is 3.  It is the last digit of the cube of 7,
so, cube root of 4913 = 17

12167:

It lies between $20^3$ = 8000 and $30^3$ = 27000 and it’s last digit, 7.  It is the last digit of the cube of 3,
so, cube root of 12167 = 23