\[\sqrt{8 + 4\sqrt{3}} = \sqrt{6} + \sqrt{2}\]
\[\sqrt{\left( \sqrt{6} + \sqrt{2} \right)^{2}} = \sqrt{6} + \sqrt{2}\]
\[\left| \sqrt{6} + \sqrt{2} \right| = \sqrt{6} + \sqrt{2}\]
\[\sqrt{6} + \sqrt{2} = \sqrt{6} + \sqrt{2}\]
\[Что\ и\ требовалось\ доказать.\]