Question

what is the smallest number of which 5184 must be multiplied so that the product is perfect cube.

Answer 1

Factor of 5184=2*2*2*2*2*2*3*3*3*3
3 have no pair of 3 so it is the required no.
To make it in pair of 3 we have to multipy it with 3*3=9so it is the required no.