There is no perfect square number between 1 and 4. On the other hand, every number is a square - or its square roots.
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1 and 4
No. 4*4 = 16 and 5*5 = 25 So the square root of 24 must be between 4 and 5. But there is no integer between 4 and 5. So 24 is not a square number.
1, 4 and 9
The square root of 16 is ±4 which is the rational number ±(4/1)
-4