Question

RÚT GỌN

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

Answer 1

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

\(A=\sqrt{\left(4+\sqrt{15}\right)^2}\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)=\sqrt{\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right)}\left(\sqrt{4+\sqrt{15}}\right)\left(\sqrt{10}-\sqrt{6}\right)\)

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

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