[tex]\displaystyle\\Demonstram~ca~ultima~cifra~a~numarului~11^{100}+6^{1000}~este~diferita\\de~ultima~cifra~a~unui~patrat~perfect.\\U(11^{100}+66^{1000})=U(11^{100})+U(66^{1000})=1+6=7,~cum~un~patrat\\perfect~nu~are~niciodata~ultima~cifra~7~\Longrightarrow 11^{100}+66^{1000}~nu~este~patrat\\perfect \Longleftrightarrow \sqrt{11^{100}+66^{1000}}~\in\mathbb{R}-\mathbb{Q}.[/tex]
