Question

Rút gọn biểu thức sau:
1) \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)

2) \(\dfrac{\sqrt{2}-1}{\sqrt{2}+2}-\dfrac{1}{1+\sqrt{2}}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)

Answer 1

1) Ta có: \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)

\(=\dfrac{1}{2}\cdot4\sqrt{3}-2\cdot5\sqrt{3}-\sqrt{3}+5\cdot\sqrt{\dfrac{4}{3}}\)

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

\(=\dfrac{-27+10}{\sqrt{3}}\)

\(=\dfrac{-17\sqrt{3}}{3}\)

b) Ta có: \(\dfrac{\sqrt{2}-1}{\sqrt{2}+2}-\dfrac{1}{\sqrt{2}+1}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)

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

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