\(\sqrt{\left(\sqrt{2}-3\right)^2}\cdot\sqrt{11+6\sqrt{2}}\)
\(=\left|\sqrt{2}-3\right|\cdot\sqrt{3^2+2\cdot3\cdot\sqrt{2}+2}\)
\(=\left(3-\sqrt{2}\right)\cdot\sqrt{\left(3+\sqrt{2}\right)^2}\)
\(=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)=7\)