Question

Rút gọn biểu thức 

Answer 1

52:

\(=\sqrt{2}+\dfrac{1}{\sqrt{3}+\sqrt{2}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\)

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

57: 

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

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

\(=\dfrac{10\sqrt{3}+10-4\sqrt{6}-4+45+15\sqrt{5}}{20}=\dfrac{51+15\sqrt{5}+10\sqrt{3}-4\sqrt{6}}{20}\)