Question

\(\sqrt{\dfrac{\sqrt{5-\sqrt{3}}}{\sqrt{5}+\sqrt{3}}}-\sqrt{\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}}\)

Answer 1

Sửa: \(\sqrt{\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}-\sqrt{\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}}\)

\(=\sqrt{\dfrac{\left(\sqrt{5}-\sqrt{3}\right)^2}{2}}-\sqrt{\dfrac{\left(\sqrt{5}+\sqrt{3}\right)^2}{2}}\\ =\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}-\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}\\ =\dfrac{\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}}{\sqrt{2}}\\ =\dfrac{-2\sqrt{3}}{\sqrt{2}}=-\sqrt{6}\)