(111two)\(^2\) change to base 10 

(111two)\(^2\) = 1 x 2\(^2\) + 1 x 2\(^1\) + 1 x 2\(^0\) = 4 + 2 + 1 = 7

(111two)\(^2\) = 7\(^2\) = 49 in base 10 

convert 49 in base 10 to base 2

Therefore (111two)\(^2\) = 110001\(_2\)

Or solve by direct multiplication.