Final answer:
Two square numbers that have a difference of 40 are 361 and 400.
Step-by-step explanation:
To find two square numbers with a difference of 40, we can use the property of square numbers that the difference between two consecutive squares is equal to the sum of those two consecutive numbers.
Let's assume the smaller square number is x2. The larger square number would then be (x+1)2. According to the given condition, (x+1)2 - x2 = 40.
Simplifying the equation, we get 2x + 1 = 40. Solving for x, we find x = 19. Therefore, the two square numbers that have a difference of 40 are 192 = 361 and 202 = 400.