GMAT Data Sufficiency (DS) | Re: Is the positive integer y a multiple of 12?

To be honest I really do not understand it completely. Can someone answer me the following question concerning statement 1:

If y^3 is a multiple of 48*t (t some integer). Then the prime factorization gives: (2^4*3) * t. Sooo how is that exactly sufficient? I mean it is for y^3 and not for y right? Isn't it possible that if you take the cube root of y^3 the outcome is different then with y^3?

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