Question

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

Answer 1

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

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

$=(\sqrt{10}-\sqrt6)\sqrt{4+\sqrt{15}}\sqrt{16-15}$

$=\sqrt2(\sqrt5-\sqrt3)\sqrt{4+\sqrt{15}}$

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

$=(\sqrt5-\sqrt3)\sqrt{5+2\sqrt{5}.\sqrt3+3}$

$=(\sqrt5-\sqrt3)\sqrt{(\sqrt5+\sqrt3)^2}$

$=(\sqrt5-\sqrt3)(\sqrt5+\sqrt3)=5-3=2$