Rút gọn biểu thức: (a) 2căn(27/4)−căn(48/9)−25căn(75/16);

a) \[2\sqrt {\frac{{27}}{4}} - \sqrt {\frac{{48}}{9}} - \frac{2}{5}\sqrt {\frac{{75}}{{16}}} \]

\[ = \frac{{2.\left( {3\sqrt 3 } \right)}}{2} - \frac{{4\sqrt 3 }}{3} - \frac{2}{5}.\frac{{5\sqrt 3 }}{4} = 3\sqrt 3 - \frac{{4\sqrt 3 }}{3} - \frac{{\sqrt 3 }}{2} = \left( {3 - \frac{4}{3} - \frac{1}{2}} \right)\sqrt 3 = \frac{{7\sqrt 3 }}{6}\];

b) \[\left( {\sqrt {99} - \sqrt {18} - \sqrt {11} } \right).\sqrt {11} + 3\sqrt {22} \]

\[\sqrt {99} .\sqrt {11} - \sqrt {18} .\sqrt {11} - \sqrt {11} .\sqrt {11} + 3\sqrt {22} = 33 - 3\sqrt {22} - 11 + 3\sqrt {22} = 22\];

c) \[\left( {\sqrt 5 + \sqrt 3 } \right).\sqrt {8 - 2\sqrt {15} } = \left( {\sqrt 5 + \sqrt 3 } \right)\sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} = \left( {\sqrt 5 + \sqrt 3 } \right)\left( {\sqrt 5 - \sqrt 3 } \right) = 5 - 3 = 2\];

d) \[\left( {\sqrt {48} - 2\sqrt 3 + 2\sqrt 4 } \right).\sqrt 5 - 2\sqrt {45} :\sqrt 3 \]

\[ = \left( {\sqrt {48} .\sqrt 5 - 2\sqrt 3 .\sqrt 5 + 2\sqrt 4 .\sqrt 5 } \right) - \left( {2\sqrt {45} :\sqrt 3 } \right)\]

\[4\sqrt {15} - 2\sqrt {15} + 4\sqrt 5 - 2\sqrt {15} = 4\sqrt 5 \].