68 of them.
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1900
100 is a perfect square of 10.The square root of 1000 is 31.6blahblahblah, so the square of 31 is less than 1000 and the square of 32 is more than 1000.That means the perfect squares between (not including) 100 and 1000 are the squares of 11 through 31, a total of 21 different values.
There are 2828 integers between 1000 and 9999.
683 perfect squares.
Infinitely many, since every positive number is a square of some other number. However, there are 21 perfect squares (SQUARES OF INTEGERS). From 112 to 312, inclusive.