Answer:
6
Step-by-step explanation:
[tex]\frac{\sqrt{(5+\sqrt{11})^{2} + (5-\sqrt{11})^{2}}}{\sqrt{2} } = \frac{\sqrt{25 + 10\sqrt{11} + 11 + 25 - 10\sqrt{11} + 11}}{\sqrt{2} } = \frac{\sqrt{72}}{\sqrt{2} } = \frac{\sqrt{72} * \sqrt{2} }{\sqrt{2} * \sqrt{2} } = \frac{\sqrt{144} }{2} = \frac{12}{2} = 6[/tex]
