Ta có: \(\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
\(=\left(\sqrt{2}.\sqrt{4+\sqrt{15}}\right).\left(\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}\right).\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{8+2\sqrt{15}}.\left(16-15\right).\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{\sqrt{5}+2\sqrt{5}.\sqrt{3}+\sqrt{3}}.\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}.\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\left(\sqrt{5}+\sqrt{3}\right).\left(\sqrt{5}-\sqrt{3}\right)\)
\(=5-3=2\)
Học tốt nha ^_^
