If y is a positive integer, for how many different values of y is \sqrt[3]{144\y}a whole number?

Question

If y is a positive integer, for how many different values of y is
`\sqrt[3]{144\y}`a whole number?

Answer 1

2

Step-by-step 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]