Rút gọn biểu thức: \( 5\sqrt a + 6\sqrt {\frac{a}{4}} - a\sqrt {\frac{4}{a}} + 5\sqrt {\frac{{4a}}{{25}}} \).

* Hướng dẫn giải

 \(\begin{array}{l} 5\sqrt a + 6\sqrt {\frac{a}{4}} - a\sqrt {\frac{4}{a}} + 5\sqrt {\frac{{4a}}{{25}}} \\ = 5\sqrt a + 6\sqrt {\frac{1}{4}.a} - a\sqrt {4.\frac{1}{a}} + 5\sqrt {\frac{4}{{25}}.a} \\ = 5\sqrt a + 6\sqrt {{{\left( {\frac{1}{2}} \right)}^2}.a} - a\sqrt {{2^2}.\frac{1}{a}} + 5\sqrt {{{\left( {\frac{2}{5}} \right)}^2}.a} \\ = 5\sqrt a + 6.\frac{1}{2}\sqrt a - 2a\sqrt {\frac{1}{a}} + 5.\frac{2}{5}\sqrt a \\ = 5\sqrt a + 3\sqrt a - 2a\frac{{\sqrt a }}{a} + 2\sqrt a = 5\sqrt a + 3\sqrt a - 2\sqrt a + 2\sqrt a = 8\sqrt a \end{array}\)