Question

\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}}\)

Answer 1

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

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

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

\(=\sqrt{7-4\sqrt{3}+2+\sqrt{3}}\)

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