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If y is a positive integer, for how many different values of y is, ∛144/y a whole number?

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Answer:

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2 different values

Therefore, "y" must be a factor of 144. Therefore, for 2 different values of "y" ( and ) is a whole number  

example

We need the remember that:

Therefore, the radicand (In this case ) must be a perfect cube in order to get a whole number.

Remember that a perfect cube are the numbers that have exact cube roots. Therefore, "y" must be a factor of 144.

Now, we need to descompose 144 into its prime factors:

Then, the factors of 144 are:

Substitute values into  to check:

mstha388

for 2 different values of "y" ( and ) is a whole number.

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