Question

Is 1188 a perfect cube . if not by which smallest natural number should 1188 be divided so that the quotient is a perfect cube

Answer 1

1188 = 2 * 2 * 11 * 3 * 3 * 3

11 has only 1 factor present so 11 must be one of the things you divide by
2 * 2 = 4 is another one. In order to have a perfect cube you need 3 prime factors not just 2

So 1188  must be divided by 11 * 4 = 44
When you do that, you get 27 which is a perfect cube.