Question

[Khuất Gia Định]

Answer 1

[HT.Phong (9A5)]

\(\sqrt{3+\sqrt{5}}\cdot\sqrt{2}\)

\(=\sqrt{2\cdot\left(3+\sqrt{5}\right)}\)

\(=\sqrt{6+2\sqrt{5}}\)

\(=\sqrt{\left(\sqrt{5}\right)^2+2\cdot\sqrt{5}\cdot1+1^2}\)

\(=\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=\left|\sqrt{5}+1\right|\)

\(=\sqrt{5}+1\)