[tex]a=\sqrt{11+6\sqrt2}\cdot \sqrt{11-6\sqrt2}+ \sqrt{11+6\sqrt2}+ \sqrt{11-6\sqrt2}\\
*\sqrt{11\pm 6\sqrt2}=\sqrt{9+2\pm 6\sqrt2}=\sqrt{(3\pm \sqrt2)^2}=|3\pm \sqrt2|=3\pm \sqrt2\\
Revenind:\\
a=\sqrt{(11-6\sqrt2)(11+6\sqrt2)}+3+\sqrt2+3-\sqrt2\\
a=\sqrt{121-72}+6\\
a=\sqrt{49}+6\\
a=7+6\Rightarrow \boxed{a=13}[/tex]
