Đáp án:
$\begin{array}{l}
a)\left( {2\sqrt 6 - 4\sqrt 3 + 5\sqrt 2 - \dfrac{1}{4}\sqrt 8 } \right).3\sqrt 6 \\
= \left( {2\sqrt 6 - 4\sqrt 3 + 5\sqrt 2 - \dfrac{1}{4}.2\sqrt 2 } \right).3\sqrt 6 \\
= \left( {2\sqrt 6 - 4\sqrt 3 + \dfrac{9}{2}\sqrt 2 } \right).3\sqrt 6 \\
= 2\sqrt 6 .3\sqrt 6 - 4\sqrt 3 .3\sqrt 6 + \dfrac{9}{2}\sqrt 2 .3\sqrt 6 \\
= 36 - 36\sqrt 2 + 27\sqrt 3 \\
b)\left( {\sqrt {\dfrac{1}{7}} - \sqrt {\dfrac{{16}}{7}} + \sqrt 7 } \right):\sqrt 7 \\
= \left( {\dfrac{{\sqrt 7 }}{7} - \dfrac{{4\sqrt 7 }}{7} + \sqrt 7 } \right):\sqrt 7 \\
= \dfrac{1}{7} - \dfrac{4}{7} + 1\\
= \dfrac{4}{7}\\
c){\left( {\sqrt {3 - \sqrt 5 } + \sqrt {3 + \sqrt 5 } } \right)^2}\\
= 3 - \sqrt 5 + 2\sqrt {3 - \sqrt 5 } .\sqrt {3 + \sqrt 5 } + 3 + \sqrt 5 \\
= 6 + 2\sqrt {{3^2} - 5} \\
= 6 + 2\sqrt 4 \\
= 6 + 2.2\\
= 10
\end{array}$
