Question

The smallest positive integer value of m in which ³√ 180 x 784 x m = a whole number

Answer 1

For the third root to be a whole number, the radicand must be a perfect cube.\[\sqrt[3]{180(784)m}=\sqrt[3]{2^6(3^2)(5)(7^2)m}=4\sqrt[3]{3^2(5)(7^2)m}\]

Answer 2

\[m=3(5^2)(7)\]