If x, y and z are real numbers such that (x - 3)² + (y - 4)² + (z - 5)² = 0, then (x + y + z) is equal to?

This is possible only when
$$\eqalign{ & {\left( {x - 3} \right)^2} = 0 \cr & x = 3 \cr & {\left( {y - 4} \right)^2} = 0 \cr & y = 4 \cr & {\left( {z - 5} \right)^2} = 0 \cr & z = 5 \cr & {\text{Then, }}\left( {x + y + z} \right) \cr & = 3 + 4 + 5 \cr & = 12 \cr} $$