Question

If y is a positive integer, for how many different values of y is RootIndex 3 StartRoot StartFraction 144 Over y EndFraction EndRoot a whole number?.

Answer 1

The value of y will be 18 or 144.

Given information:

The given expression is $\sqrt[3]{\frac{144}{y} }$.

It is required to find the values of y which are whole numbers.

Now, factorize 144 as,

$144=2\times2\times2\times2\times3\times3\\144=2^3\times2\times3\times3$

So, for the value of given expression to be a whole number, the value of y should be,

$2\times3\times3=18$ or 144.

For the above values of y, the given expression will be,

$\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{18} }\\=\sqrt[3]{8} =2\\\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{144} }\\=\sqrt[3]{1} \\=1$

Therefore, the value of y will be 18 or 144.

For more details, refer to the link:

brainly.com/question/17429689