Đặt \(A=\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)
\(=\left(\sqrt{4+\sqrt{15}}\right)\left(\sqrt{4-\sqrt{15}}\right)\left(\sqrt{4+\sqrt{15}}\right)\left(\sqrt{10}-\sqrt{6}\right)\)
\(=\sqrt{4+\sqrt{15}}.\left(\sqrt{10}-\sqrt{6}\right)\)
\(=\frac{\sqrt{8+2\sqrt{15}}}{\sqrt{2}}.\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{8+2\sqrt{15}}.\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}.\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=2\)
\(\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}=\left(\sqrt{10}-\sqrt{6}\right).\sqrt{\left(4+\sqrt{15}\right)^2\left(4-\sqrt{15}\right)}=\left(\sqrt{10}-\sqrt{6}\right).\sqrt{\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right).\left(4+\sqrt{15}\right)}=\left(\sqrt{10}-\sqrt{6}\right).\sqrt{\left(16-15\right)\left(4+\sqrt{15}\right)}=\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4+\sqrt{15}}.\sqrt{2}=\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8+2\sqrt{15}}=\left(\sqrt{5}-\sqrt{3}\right)\sqrt{5+2.\sqrt{5}.\sqrt{3}+3}=\left(\sqrt{5}-\sqrt{3}\right)\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)=5-3=2\)
