Question

\(\sqrt{4-\sqrt{15}}\) (\(\sqrt6\) +\(\sqrt{10}\) )

Answer 1

Ta có: \(\sqrt{4-\sqrt{15}}\left(\sqrt6+\sqrt{10}\right)\)

\(=\sqrt{8-2\sqrt{15}}\left(\sqrt3+\sqrt5\right)\)

\(=\sqrt{\left(\sqrt5-\sqrt3\right)^2}\cdot\left(\sqrt5+\sqrt3\right)\)

\(=\left(\sqrt5-\sqrt3\right)\left(\sqrt5+\sqrt3\right)=5-3=2\)