\(=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)\sqrt{10-2\sqrt{21}}\)
\(=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\left(5+\sqrt{21}\right)\left(10-2\sqrt{21}\right)\)
\(=2\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)\)
\(=2\left(25-21\right)=8\)
\(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
\(=\sqrt{5+\sqrt{21}}\sqrt{5-\sqrt{21}}\sqrt{5+\sqrt{21}}\sqrt{2}\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{4}\sqrt{10+2\sqrt{21}}\left(\sqrt{7}-\sqrt{3}\right)\)
\(=2\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\left(\sqrt{7}-\sqrt{3}\right)\)
\(=2\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=2\left(7-3\right)=2.4=8\)