Question

Answer 1

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

\(=\sqrt{3^2-\left(\sqrt{5+2\sqrt{3}}\right)^2}\)\(=\sqrt{9-5-2\sqrt{3}}=\sqrt{4-2\sqrt{3}}=\sqrt{3-2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)

Answer 2

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

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

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

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