A number AABB is the square of an integer. Find this integer, aided by pen and paper. No other calculating aids allowed.

A number AABB may be written as 11*(100A + B), where A and B are integers between 1 and 9.

If 11*(100A+B) is a square, then 100A+B must be divisible by 11. Indeed, (100A+B)/11 must be a square, too.

If we take A = 7 and B = 4, then 100A+B = 704 = 11*64 = 11*(8^2).

(I've tried some values and noticed that 7 and 4 would satisfy the conditions.)

In fact, we have 7744 = 88^2.