Đáp án:
$8+2\sqrt{5}$
Giải thích các bước giải:
$(4+\sqrt{5})(\sqrt{10}+\sqrt{6})\sqrt{4-\sqrt{15}}\\ =(4+\sqrt{5})(\sqrt{5}+\sqrt{3}).\sqrt{2}.\sqrt{4-\sqrt{15}}\\ =(4+\sqrt{5})(\sqrt{5}+\sqrt{3})\sqrt{8-2\sqrt{15}}\\ =(4+\sqrt{5})(\sqrt{5}+\sqrt{3})\sqrt{5-2\sqrt{5}.\sqrt{3}+3}\\ =(4+\sqrt{5})(\sqrt{5}+\sqrt{3})\sqrt{(\sqrt{5}-\sqrt{3})^2}\\ =(4+\sqrt{5})(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})\\ =(4+\sqrt{5})(5-3)\\ =2(4+\sqrt{5})\\ =8+2\sqrt{5}$
