\[\sqrt{9 - 6\sqrt{2}} = \sqrt{6} - \sqrt{3}\]
\[\sqrt{9 - 6\sqrt{2}} =\]
\[= \sqrt{3 - 2\sqrt{3} \cdot \sqrt{6} + 6} =\]
\[= \sqrt{\left( \sqrt{3} - \sqrt{6} \right)^{2}} = \sqrt{6} - \sqrt{3}\]