Question: aabb is a perfect square?
Answer: To be a perfect square, each factor must appear an even number of times. Then (100a+b) must be a multiple of 11, which in this case is achieved by making that a+b=11. So, the possibles a and b are 9 and 2, 8 and 3, 7 and 4, 6 and 5, or the opposite order.