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

AABB=m*m

11*A0B=m*m => 11|A0B

Because condition that number can be devided by 11 in decade number system is a0+a2+a4+...+a2i=a1+a3+a5+a(2i+1) we get A+B=0; Since A>=0 and B>=0 we get A=0 and B=0; so thet number does not exist.