Question

m.n làm bằng cách đặt nhân tử chung của vế giữa thử đi ạ

(\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)

Answer 1

ta có: \(\left(4+\sqrt{15}\right)\sqrt{2\left(\sqrt{5}-\sqrt{3}\right)}\sqrt{4-\sqrt{15}}\)

\(=\left(4+\sqrt{15}\right)(\sqrt{5}-\sqrt{3})\sqrt{8-2\sqrt{3}.\sqrt{5}}\)

\(=\frac{\left(8+2\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{2}\)

\(=\frac{\left(\sqrt{5}+\sqrt{3}\right)^2\left(\sqrt{5}-\sqrt{3}\right)^2}{2}\)

\(=\frac{\left(5-3\right)^2}{2}=2\)