Hãy rút gọn biểu thức: \(\dfrac{3}{2}\sqrt 6+ 2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\)

* Hướng dẫn giải

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

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

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

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

\(=3\dfrac{\sqrt 6 .3}{2.3}+2\dfrac{\sqrt 6 .2}{3.2}-4\dfrac{\sqrt 6 .3}{2.3}\)

\(=9\dfrac{\sqrt 6}{6}+4\dfrac{\sqrt 6}{6}-12\dfrac{\sqrt 6}{6}\)

\(=(9+4-12)\dfrac{\sqrt 6}{6}=\dfrac{\sqrt 6}{6}\)