\(\left(\sqrt{10}+\sqrt{2}\right)\sqrt{3+\sqrt{5}}\cdot\left(3-\sqrt{5}\right)\)
\(=\sqrt{2}\left(\sqrt{5}+1\right)\sqrt{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}\cdot\sqrt{3-\sqrt{5}}\)
\(=\sqrt{2}\cdot\left(\sqrt{5}+1\right)\cdot\sqrt{3-\sqrt{5}}\cdot\sqrt{9-5}\)
\(=\sqrt{6-2\sqrt{5}}\cdot\left(\sqrt{5}+1\right)\cdot\sqrt{4}\)
\(=\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1^2}\cdot\left(\sqrt{5}+1\right)\cdot2\)
\(=\left|\sqrt{5}-1\right|\cdot\left(\sqrt{5}+1\right)\cdot2\)
\(=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)\cdot2\)
\(=\left(5-1\right)\cdot2\)
\(=8\)
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