a) \(\sqrt {\frac{{11}}{6}} = \sqrt {\frac{{11.6}}{{6.6}}} = \frac{{\sqrt {66} }}{{\sqrt {{6^2}} }} = \frac{{\sqrt {66} }}{6}\)
b) \(a\sqrt {\frac{2}{{5a}}} = a.\sqrt {\frac{{2.5a}}{{5a.5a}}} = a.\frac{{\sqrt {10a} }}{{\sqrt {{{(5a)}^2}} }} = a.\frac{{\sqrt {10a} }}{{5\left| a \right|}}\)
Vì a > 0 nên \(a.\sqrt {\frac{2}{{5a}}} = a.\frac{{\sqrt {10a} }}{{5a}} = \frac{{\sqrt {10a} }}{{5}}\)
c) \(4x\sqrt {\frac{3}{{4xy}}} = 4x\sqrt {\frac{{3.4xy}}{{4xy.4xy}}} = 4x\frac{{\sqrt {12xy} }}{{\sqrt {{{\left( {4xy} \right)}^2}} }} = \frac{{8x\sqrt {3xy} }}{{\left| {4xy} \right|}}\)
Vì x > 0; y > 0 nên \(4x\sqrt {\frac{3}{{4xy}}} = \frac{{8x\sqrt {3xy} }}{4xy} = \frac{{2\sqrt {3xy} }}{y}\)