\(\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\cdot\sqrt{3-\sqrt{5}}\)
\(=\left(3+\sqrt{5}\right)\cdot\left(\sqrt{5}-1\right)\cdot\sqrt{2}\cdot\sqrt{3-\sqrt{5}}\)
\(=\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{6-2\sqrt{5}}\)
\(=\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\cdot\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=\left(3+\sqrt{5}\right)\cdot\left(\sqrt{5}-1\right)^2\)
\(=\left(3+\sqrt{5}\right)\left(6-2\sqrt{5}\right)\)
\(=2\cdot\left(3+\sqrt{5}\right)\cdot\left(3-\sqrt{5}\right)\)
\(=2\cdot\left(9-5\right)\)
\(=2-4=8\)
\(\left(3+\sqrt{5}\right)\left(\sqrt{10-\sqrt{2}}\right)\sqrt{3-\sqrt{5}}\)
\(\Rightarrow\left(3\sqrt{10}-3\sqrt{2}+\sqrt{50}-\sqrt{10}\right)\sqrt{3-\sqrt{5}}\)
\(\Rightarrow\left(3\sqrt{10}-3\sqrt{2}+5\sqrt{2}-\sqrt{10}\right)\sqrt{3-\sqrt{5}}\)
\(\Rightarrow\left(2\sqrt{10}+2\sqrt{2}\right)\sqrt{3-\sqrt{5}}\)
\(\Rightarrow2\sqrt{10\left(3-\sqrt{5}\right)}+2\sqrt{2\left(3-\sqrt{5}\right)}\)
\(\Rightarrow2\sqrt{30-10\sqrt{5}}+2\sqrt{6-2\sqrt{5}}\)
\(\Rightarrow2\sqrt{\left(5-\sqrt{5}\right)^2}+2\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(\Rightarrow2\left(5-\sqrt{5}\right)+2\left(\sqrt{5-1}\right)\)
\(\Rightarrow10-2\sqrt{5}+2\sqrt{5}-2\)
\(\Rightarrow8\)
