\[\begin{array}{l} {\text{Проверьте тождество:}} \hfill \\ \sqrt[4]{{\sqrt {\frac{1}{6}} + \sqrt {\frac{1}{8}} }} + \sqrt[4]{{\sqrt {\frac{1}{6}} - \sqrt {\frac{1}{8}} }} = \sqrt[4]{{2 + \frac{{5\sqrt 6 }}{6}}}. \hfill \\ \end{array}\]