Đáp án:
$\begin{array}{l}
a)2\sqrt 3 \left( {\sqrt {27} + 2\sqrt {48} - \sqrt {25} } \right) + \sqrt {300} \\
= 2\sqrt 3 .3\sqrt 3 + 2\sqrt 3 .2.4\sqrt 3 - 2\sqrt 3 .5 + 10\sqrt 3 \\
= 18 + 48 - 10\sqrt 5 + 10\sqrt 5 \\
= 66\\
b)\left( {2 + \sqrt 3 - \sqrt 5 } \right)\left( {2 + \sqrt 3 + \sqrt 5 } \right)\\
= {\left( {2 + \sqrt 3 } \right)^2} - 5\\
= 4 + 4\sqrt 3 + 3 - 5\\
= 2 + 4\sqrt 3 \\
c)\left( {1 + \dfrac{{5 - \sqrt 5 }}{{1 - \sqrt 5 }}} \right)\left( {\dfrac{{5 + \sqrt 5 }}{{1 + \sqrt 5 }} + 1} \right)\\
= \left( {1 - \sqrt 5 } \right)\left( {\sqrt 5 + 1} \right)\\
= 1 - 5\\
= - 4\\
d)3\sqrt {\dfrac{9}{8}} - \sqrt {\dfrac{{49}}{2}} + \dfrac{2}{{1 - \sqrt 2 }}\\
= 3.\dfrac{3}{{2\sqrt 2 }} - \dfrac{7}{{\sqrt 2 }} + \dfrac{{2\left( {1 + \sqrt 2 } \right)}}{{1 - 2}}\\
= \dfrac{{9\sqrt 2 }}{4} - \dfrac{{7\sqrt 2 }}{2} - 2 - 2\sqrt 2 \\
= \dfrac{{ - 5\sqrt 2 }}{4} - 2 - 2\sqrt 2 \\
= \dfrac{{ - 13\sqrt 2 - 8}}{4}\\
e)\left( {\sqrt {72} - 2\sqrt 2 + 3\sqrt 5 } \right)\sqrt 2 - \sqrt {90} \\
= \left( {6\sqrt 2 - 2\sqrt 2 + 3\sqrt 5 } \right)\sqrt 2 - 3\sqrt {10} \\
= \left( {4\sqrt 2 + 3\sqrt 5 } \right)\sqrt 2 - 3\sqrt {10} \\
= 8 + 3\sqrt {10} - 3\sqrt {10} \\
= 8\\
f)2\sqrt 3 \left( {\sqrt {27} + 2\sqrt {48} - \sqrt {25} } \right) + \sqrt {300} \\
= 2\sqrt 3 .3\sqrt 3 + 2\sqrt 3 .2.4\sqrt 3 - 2\sqrt 3 .5 + 10\sqrt 3 \\
= 18 + 48 - 10\sqrt 5 + 10\sqrt 5 \\
= 66
\end{array}$
