4 and 5
The square numbers between 1 and 20 are 1,4,9 and 16.
All whole numbers between 1 and 400 (=20 square).
23, 29
There are an infinite number of rational numbers between any two numbers.
25
There are (not counting 1) three square numbers between 1 and 20.
20 is a whole number and so it cannot lie between two consecutive whole numbers.
There are 31 perfect square numbers between 1 and 1000 (including 1).
4
25, 49, 81 To satisfy your criterion, you need the square of an odd number.
They are 25, 36, 49, 64, and 81 .