Question

If y is a positive integer, for how many different values of y is id="TexFormula1" title="\sqrt[3]{144\y}" alt="\sqrt[3]{144\y}" align="absmiddle" class="latex-formula">a whole number?

Answer 1

Answer:

2

Explanation:

I'll explain later, it has to do with prime factors, and perfect cubes.

The two values of y that work are 18, and 144.

³√(144/18) = ³√(8) = 2 [whole number]

³√(144/144) = ³√(1) = 1 [whole number]