Question

The smallest number by which 192 should be multiplied to make it a perfect cube is

Answer 1

`9`

Explanation:

The prime factorization of
`192` is
`2^6 \cdot 3`, and since
`2^6` is already a perfect cube of
`4`, we just have to deal with the
`3`. To make it a perfect cube, we have to multiply
`3` three times, and so we have to make it
`3 \cdot 3 \cdot 3`, and we already have one three so we just add the other two threes, which equal
`3^2=9`.