They are: 1 4 9 16 25 36 49 and 64
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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.
perfect square
64. 4x4x4 and 8x8
What are the integers between 0 and 100 whose positive square roots are integers?
perfect squares