The difference between consecutive perfect square numbers is always odd...?

Answer 1

The difference between consecutive squares is always an odd number.

If n is any natural number then the difference between the square of n and the square of the next natural number, (n + 1) is 2n + 1, which is an odd number.

( n² + 2n + 1 ) - n² = 2n + 1

Answer 2

If n² a perfect square, then the next largest perfect square is (n +1)² = n² + 2n + 1.

This makes their difference 2n + 1, an odd integer.

(Visually, you can imagine a square array of dots. To construct the next biggest square array, you will need to add the same number of dots to the top and right side as are there, plus one more for the top right corner.)