\[\begin{array}{l} {\text{Упростите:}} \hfill \\ \sqrt[3]{{\frac{{27 + 11\sqrt 6 }}{{72}}}} + \sqrt[3]{{\frac{{27 - 11\sqrt 6 }}{{72}}}}. \hfill \\ \end{array}\]

\[\begin{array}{l} {\text{Упростите:}} \hfill \\ \sqrt[4]{{\frac{{3 + 2\sqrt[4]{2}}}{{3 - 2\sqrt[4]{2}}}}} + \sqrt[4]{{\frac{{3 - 2\sqrt[4]{2}}}{{3 + 2\sqrt[4]{2}}}}}. \hfill \\ \end{array}\]

\[\begin{array}{l} {\text{Проверьте тождество:}} \hfill \\ \sqrt[4]{{\frac{{11 + 6\sqrt[4]{{10}}}}{{11 - 6\sqrt[4]{{10}}}}}} = \frac{1}{{41}}\left( {\sqrt {1189 + 451\sqrt {10} } + \sqrt {2870 + 451\sqrt {10} } } \right). \hfill \\ \end{array}\]