\[\left( \sqrt{9 - 4\sqrt{5}} - \sqrt{9 + 4\sqrt{5}} \right)^{2} =\]
\[= 18 - 2\sqrt{81 - 16 \cdot 5} =\]
\[= 18 - 2\sqrt{81 - 80} =\]
\[= 18 - 2\sqrt{1} = 18 - 2 = 16\]