Question

The difference between consecutive perfect square numbers is always odd.

Options:
A) True
B) False

Answer 1

The difference between consecutive perfect squares is always an odd number, represented mathematically by the expression 2n + 1, where n is an integer.

Step-by-step explanation:

The difference between consecutive perfect squares is indeed always an odd number. We can prove this mathematically by considering two consecutive perfect squares, which can be represented as n² and (n+1)². The difference between these two squares is:

(n+1)² - n² = n² + 2n + 1 - n² = 2n + 1

This result, 2n + 1, is always an odd number because it is the sum of an even number (2n) and 1. Thus, the statement is True.