Lời giải:Ta có:
\(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
\(=\dfrac{1}{2}\sqrt{16. 3}-2\sqrt{25. 3}-\dfrac{\sqrt{3.11}}{\sqrt{11}}+5\sqrt{\dfrac{1.3+1}{3}}\)
\(=\dfrac{1}{2}\sqrt{4^2. 3}-2\sqrt{5^2. 3}-\dfrac{\sqrt 3.\sqrt{11}}{\sqrt{11}}+5\sqrt{\dfrac{4}{3}}\)
\(=\dfrac{1}{2}.4\sqrt{ 3}-2.5\sqrt{3}-\sqrt{3}+5\dfrac{\sqrt 4}{\sqrt 3}\)
\(=\dfrac{4}{2}\sqrt{ 3}-10\sqrt{3}-\sqrt{3}+5\dfrac{\sqrt{4}.\sqrt 3}{\sqrt{3}.\sqrt {3}}\)
\(=2\sqrt{ 3}-10\sqrt{3}-\sqrt{3}+5\dfrac{2\sqrt{3}}{3}\)
\(=2\sqrt{ 3}-10\sqrt{3}-\sqrt{3}+10\dfrac{\sqrt{3}}{3}\)
\(= \left( {2 - 10 - 1 + \dfrac{10}{3} }\right)\sqrt 3 \)
\(=-\dfrac{17}{3}\sqrt 3\).
