Question

Answer 1

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

\(=\sqrt{9-\left(5+2\sqrt{3}\right)}\)

\(=\sqrt{4-2\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)

Answer 2

Ta có: \(\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}\)

\(=\sqrt{9-5-2\sqrt{3}}\)

\(=\sqrt{4-2\sqrt{3}}\)

\(=\sqrt{3}-1\)