4, 9, 16 and 25
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There are 2 prime numbers between 30 and 40: 31 and 37.
There are 2*13 = 26 natural numbers between them.
The square root of 31 falls between the whole numbers 5 and 6.
There are 16 square numbers between 1 and 300: 2 to 17 inclusive. There is no square root of these numbers: only of their sum or product or average or some other operation.