\[\begin{array}{l} {\text{Проверьте тождество:}} \hfill \\ \sqrt {\sqrt {\frac{1}{2}} + \sqrt {\frac{1}{3}} } + \sqrt {\sqrt {\frac{1}{2}} - \sqrt {\frac{1}{3}} } = \sqrt[4]{{\frac{{8 + 4\sqrt 3 }}{3}}}. \hfill \\ \end{array}\]