Question

Найдите значение выражения

Answer 1

$(4+\sqrt{15})(\sqrt{10}-\sqrt6})\sqrt{4-\sqrt{15}} = (4\sqrt{10} -4\sqrt6+\sqrt{150}-\sqrt{90})\sqrt{4-\sqrt{15}} = \\\\= (4\sqrt{10} -4\sqrt6+5\sqrt6-3\sqrt{10})\sqrt{4-\sqrt{15}} = (\sqrt{10}+\sqrt6)\sqrt{4-\sqrt{15}} = \\ \\=(\sqrt{10(4-\sqrt{15}})+\sqrt{6(4-\sqrt{15}}) = \sqrt{40-10\sqrt{15}} + \sqrt{24-6\sqrt{15}} = \\\\=\sqrt{(5-\sqrt{15})^2}+\sqrt{(3-\sqrt{15})^2} = 5-\sqrt{15}+\sqrt{15}-3 = 2$