Question

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

Answer 1

\(\left(\sqrt{\text{1}0}-\sqrt{6}\right)\cdot\left(4+\sqrt{15}\right)\cdot\sqrt{4-\sqrt{15}}\)

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

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

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

\(=\sqrt{\left(10+6+2\sqrt{60}\right)\left(4-\sqrt{15}\right)}\)

\(=\sqrt{\left(16+4\sqrt{15}\right)\left(4-\sqrt{15}\right)}\)

\(=\sqrt{64-16\sqrt{15}+16\sqrt{15}-60}\)

\(=\sqrt{4}=2\)