If xxyy is a perfect square then x + y =?
11
xxyy = xx00 + yy = 11(x00 + y) = 11(x0y)
xxyy is a perfect square, so if one divisor is 11, then there should be one more 11 to get 112.
As xxyy = 11(x0y), x0y should be divisible by 11, so x + y has to 11.