450y = n^3
450 = 2 x 3 x 3 x 5 x 5
Since y and n are positive integers, y must atleast have 2 x 2 x 3 x 5 to complete the cubes.
So, only (I) must be an integer.
By picking numbers, let y = 60, n^3 = 450 * 60 = 27000. n = 30
(I) = 1
(II) = 2/3
(III) = 2/5
So, only (I) is an integer.
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