\(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
\(=\sqrt{6-2\sqrt{5}}\cdot\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)\)
\(=\left(6-2\sqrt{5}\right)\left(3+\sqrt{5}\right)\)
\(=18+6\sqrt{5}-6\sqrt{5}-20=-2\)
\(\left(\sqrt{6}+\sqrt{2}\right)\left(4-2\sqrt{3}\right)\sqrt{2+\sqrt{3}}\)
\(=\left(\sqrt{3}+1\right)\cdot\sqrt{4+2\sqrt{3}}\left(4-2\sqrt{3}\right)\)
\(=\left(\sqrt{3}+1\right)^2\left(4-2\sqrt{3}\right)\)
\(=\left(4+2\sqrt{3}\right)\left(4-2\sqrt{3}\right)=16-12=4\)
\(\left(4-\sqrt{15}\right)\left(\sqrt{6}+\sqrt{10}\right)\sqrt{4+\sqrt{15}}\)
\(=\left(4-\sqrt{15}\right)\left(\sqrt{5}+\sqrt{3}\right)\cdot\sqrt[]{8+2\sqrt{15}}\)
\(=\left(4-\sqrt{15}\right)\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)\)
\(=\left(4-\sqrt{15}\right)\left(8+2\sqrt{15}\right)=32-8\sqrt{15}+8\sqrt{15}-30=2\)
