Question

\(\sqrt{\dfrac{5}{2}}+\dfrac{\sqrt{2}}{3+\sqrt{5}}\) tính giá trị biểu thức

\(\dfrac{3+4\sqrt{3}}{\sqrt{6}+\sqrt{2}-\sqrt{5}}+\dfrac{2\sqrt{2}}{1-\sqrt{3}}\)

Answer 1

a: \(=\dfrac{\sqrt{10}}{2}+\dfrac{\sqrt{2}\left(3-\sqrt{5}\right)}{4}\)

\(=\dfrac{2\sqrt{10}+3\sqrt{2}-\sqrt{10}}{4}=\dfrac{\sqrt{10}+3\sqrt{2}}{4}\)

b: \(\dfrac{3+4\sqrt{3}}{\sqrt{6+2\sqrt{5}}}-\dfrac{2\sqrt{2}\left(\sqrt{3}+1\right)}{2}\)

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

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

\(=\dfrac{4\sqrt{15}-4\sqrt{3}+3\sqrt{5}-3-4\sqrt{6}-4\sqrt{2}}{4}\)