Đáp án:
$\begin{array}{l}
a)A = 2\sqrt 3 \left( {\sqrt 3 - 2} \right) + 4\sqrt 3 \\
= 2\sqrt 3 .\sqrt 3 - 4\sqrt 3 + 4\sqrt 3 \\
= 2.3\\
= 6\\
b)B = 2\sqrt {{{\left( {2 + \sqrt 5 } \right)}^2}} - \sqrt {20} \\
= 2.\left( {2 + \sqrt 5 } \right) - 2\sqrt 5 \\
= 4 + 2\sqrt 5 - 2\sqrt 5 \\
= 4\\
c)C = \sqrt 2 .\sqrt {7 - 3\sqrt 5 } + \sqrt 5 \\
= \sqrt {14 - 2.3.\sqrt 5 } + \sqrt 5 \\
= \sqrt {9 - 2.3.\sqrt 5 + 5} + \sqrt 5 \\
= \sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} + \sqrt 5 \\
= 3 - \sqrt 5 + \sqrt 5 \\
= 3\\
d)D = \frac{{\sqrt {10} - \sqrt 2 }}{{\sqrt 5 - 1}} - \frac{7}{{\sqrt 7 }} + \frac{5}{{\sqrt 7 + \sqrt 2 }}\\
= \frac{{\sqrt 2 \left( {\sqrt 5 - 1} \right)}}{{\sqrt 5 - 1}} - \sqrt 7 + \frac{{5\left( {\sqrt 7 - \sqrt 2 } \right)}}{{7 - 2}}\\
= \sqrt 2 - \sqrt 7 + \sqrt 7 - \sqrt 2 \\
= 0
\end{array}$
