When you subtract one square number from another square number the answer is 8 what are the two square numbers?

Answer 1

Let the two numbers be a and b.

Then a2 - b2 = 8

But, a2 - b2 can be factored and thus,

(a + b)(a - b) = 8

The factor pairs of 8 are (8,1) and (4,2)

Substituting these figures

1) Using (8,1) If (a + b) = 8 and (a - b) = 1 then 2a = 8 + 1 : a = 4½ and b = 3½

2) Using (4,2) If (a + b) = 4 and (a - b) = 2 then 2a = 4 + 2 : a = 3 and b = 1..........which is the integer answer that is required.

Then 32 - 12 = 9 - 1 = 8