A number AABB is the square of an integer. Find this integer, aided by pen and paper. No other calculating aids allowed.
A four digit number must have a two digit square, greater than 31 (since 31²<1000). Also, AABB is a multiple of 11, so its square root must also be a multiple of 11. The two previous conditions show that the square root must be 33, 44, 55, 66, 77, 88 or 99. Testing them by hand finds 88²=7744.
Just by hand
