[tex]\sqrt{6+\sqrt{11}}=\sqrt{\frac{6+\sqrt{6^2-11}}{2}}+\sqrt{\frac{6-\sqrt{6^2-11}}{2}}=\sqrt{\frac{6+\sqrt{36-11}}{2}}+\sqrt{\frac{6-\sqrt{36-11}}{2}}=\sqrt{\frac{11}{2}}+\sqrt{\frac{1}{2}}=\frac{\sqrt{11}}{\sqrt{2}}+\frac{1}{\sqrt2}=\frac{\sqrt{11}+1}{\sqrt2}[/tex]
