Question

Tính:

\(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)

Answer 1

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

\(=6+2\sqrt{9-5}=6+2\sqrt{4}=10\)

Answer 2

\(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)

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

\(=6+2\sqrt{9-5}=6+2\sqrt{4}=10\)