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there is an infinite number
It is a rational number - as are ALL perfect squares.
There are infinitely many, just like in base 10. In any base system, the number of perfect squares is the same. Take the natural (counting) numbers 1, 2, 3, .... Squaring each of these produces the perfect squares. As there are an infinite number of natural numbers, there are an infinite number of perfect squares. The first 10 perfect squares in base 5 are: 15, 45, 145, 315, 1005, 1215, 1445, 2245, 3115, 4005, ...
101 is aprime number....
If you have a number like 12 and you multiply it by the same number: 12 and the answer you get is a whole number, then the whole number is the perfect square.