\[\sqrt{38 - 12\sqrt{2}} = 6 - \sqrt{2}\]
\[\sqrt{\left( 6 - \sqrt{2} \right)^{2}} = 6 - \sqrt{2}\]
\[\left| 6 - \sqrt{2} \right| = 6 - \sqrt{2}\]
\[6 - \sqrt{2} = 6 - \sqrt{2}\]
\[Что\ и\ требовалось\ доказать.\]