[tex]\displaystyle Avem:~6+4 \sqrt{2}=2+4 \sqrt{2}+4=(\sqrt{2})^2+2 \cdot \sqrt{2} \cdot 2+2^2= \\ \\ =( \sqrt{2}+2)^2. \\ \\ 7+5 \sqrt{2}=1+3 \sqrt{2}+ 6+2\sqrt{2}=1^3+3 \cdot 1^2 \cdot \sqrt{2}+3 \cdot 1 \cdot (\sqrt{2})^2+ \\ \\ +(\sqrt{2})^3=(1+ \sqrt{2})^3. \\ \\ a=\sqrt{(\sqrt{2}+2)^2}+ \sqrt[3]{(1+\sqrt{2})^3} =|\sqrt{2}+2}|+ 1+\sqrt{2}=2 \sqrt{2}+3= \\ \\ =( \sqrt{2}+1)^2. \\ \\ Numarul~nu~este~patrat~perfect.~Un~patrat~perfect~este~patratul~ \\ \\ unui~numar~intreg.[/tex]
