Yes.
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Zero is a rational number and an integer.
The number zero is both a integer and a whole number. This is taught in math.
I have never before heard of a non-perfect square but I suppose it would be any non-zero number that is not the square of an integer. People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."
Divide a non-zero integer by a non-zero integer.
How about zero = 0 which is an integer but not a whole number