Question

Tính : \(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)

Answer 1

\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\\ =\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}.\sqrt{3+\sqrt{5}}.\sqrt{2}\left(\sqrt{5}-1\right)\\ =\sqrt{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}.\sqrt{6+2\sqrt{5}}.\left(\sqrt{5}-1\right)\\ =\sqrt{9-5}.\sqrt{\left(\sqrt{5}+1\right)^2}\left(\sqrt{5}-1\right)\\ =2\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)\\ =2.4\\ =8\)