What two square numbers have a difference of 40?
Let's denote the two square numbers as ( a^2 ) and ( b^2 ), where ( a ) and ( b ) are positive integers. The difference between these two square numbers can be expressed as ( b^2 - a^2 = 40 ). This can be factored as ( (b + a)(b - a) = 40 ). The factors of 40 are (1, 40), (2, 20), and (4, 10). By solving the system of equations, we find that the two square numbers are 49 and 9, as ( 7^2 - 3^2 = 49 - 9 = 40 ).