Giá trị của biểu thức: \( 2\sqrt {\frac{{16a}}{3}} - 3\sqrt {\frac{a}{{27}}} - 6\sqrt {\frac{{4a}}{{75}}} \)

* Hướng dẫn giải

 \(\begin{array}{l} 2\sqrt {\frac{{16a}}{3}} - 3\sqrt {\frac{a}{{27}}} - 6\sqrt {\frac{{4a}}{{75}}} = 2\sqrt {{4^2}.\frac{a}{3}} - 3\sqrt {\frac{1}{9}.\frac{a}{3}} - 6\sqrt {\frac{4}{{25}}.\frac{a}{3}} \\ = 2.4\sqrt {\frac{a}{3}} - 3.\frac{1}{3}\sqrt {\frac{a}{3}} - 6.\frac{2}{5}.\sqrt {\frac{a}{3}} = \sqrt {\frac{a}{3}} .\left( {8 - 1 - \frac{{12}}{5}} \right) = \frac{{23}}{5}\sqrt {\frac{a}{3}} = \frac{{23}}{5}.\frac{{\sqrt {3a} }}{3} = \frac{{23\sqrt {3a} }}{{15}} \end{array}\)