Question

What should be multiplied to 43200 to make it a perfect cube?

Answer 1

For a number to be a perfect cube, its prime factors should be in the form of triplets
By prime factorization, $43200=2^6\times 3^3\times 5^2$

The prime factorization contains only two 5’s, so we need to multiply the number with one more 5 to make it a triplet.

Also, if we multiply the number by $\frac{1}{25}$, then the two of the 5’s will be removed, leaving only the triplet factor of 2 and 3, which is again a perfect cube.

$\therefore$ The number becomes a perfect cube on multiplying with 5 or 1/25.