\[\left( 3\sqrt{5} - 2 \right)^{2} = \left( 3\sqrt{5} \right)^{2} - 2 \cdot 6\sqrt{5} + 2^{2} =\]
\[= 9 \cdot 5 - 12\sqrt{5} + 4 =\]
\[= 45 - 12\sqrt{5} + 4 = 49 - 12\sqrt{5}\]