\[A = (3\sqrt{5})^2 \quad B = (\sqrt{7})^2 \quad C = (\sqrt{5})^2 \quad D = \sqrt{11}\cdot\sqrt{11}\]
\[E = (\sqrt{5})^2+(\sqrt{5})^2 \quad F = (\sqrt{11})^2-(\sqrt{11})^2\]
\[G = (2\sqrt{3}-3\sqrt{5}+5\sqrt{2})(2\sqrt{3}-5\sqrt{2}-3\sqrt{5})\]
\[A = (3\sqrt{5})^2 = 9 \times 5 = \boxed{45}\]
\[B = (\sqrt{7})^2 = \boxed{7}\]
\[C = (\sqrt{5})^2 = \boxed{5}\]
\[D = \sqrt{11} \cdot \sqrt{11} = (\sqrt{11})^2 = \boxed{11}\]
\[E = 5+5 = \boxed{10}\]
\[F = 11-11 = \boxed{0}\]
حساب \(G\) :نُعيد ترتيب الحدين :
\[G = (2\sqrt{3}-3\sqrt{5}+5\sqrt{2})(2\sqrt{3}-3\sqrt{5}-5\sqrt{2})\]
نضع \(u = 2\sqrt{3}-3\sqrt{5}\) و \(v = 5\sqrt{2}\) :
\[G = (u+v)(u-v) = u^2-v^2\]
\[u^2 = (2\sqrt{3}-3\sqrt{5})^2 = 12-12\sqrt{15}+45 = 57-12\sqrt{15}\]
\[v^2 = (5\sqrt{2})^2 = 50\]
\[G = 57-12\sqrt{15}-50 = \boxed{7-12\sqrt{15}}\]