Any number between 64 & 81 inclusive.
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If you calculate those square roots, you can count the integers in between pretty fast.
There are 2*13 = 26 natural numbers between them.
152 = 225 and 312 = 961 so there are 16 square numbers between 200 and 1000
Because many square roots are irrational numbers that can not be computed to an exact value for lack of space to continue an infinite string of digits after the decimal point.
Infinitely many, since every number in that range is a square of some other number. There are 7 perfect square numbers.