If \(x=720\) and \(ax\) is a perfect cube where \(a\) is a positive integer, what is the smallest possible value of \(\sqrt[3]{ax}\)?
Factor 720.....
72 * 10
8 * 9 * 5 *2
2^3 * 3^2 * 5^1 * 2^1
To have a perfect cube......we need "a" to be 3 * 5^2 * 2^2 = 300
So....the smallest value is
∛ [ 720 * 300 ] = ∛ [216000] = 60
