Đáp án:
$\begin{array}{l}
a)A = \frac{{2 + \sqrt 3 }}{{2 + \sqrt {4 + 2\sqrt 3 } }} + \frac{{2 - \sqrt 3 }}{{2 - \sqrt {4 - 2\sqrt 3 } }}\\
= \frac{{2 + \sqrt 3 }}{{2 + \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} }} + \frac{{2 - \sqrt 3 }}{{2 - \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} }}\\
= \frac{{2 + \sqrt 3 }}{{2 + \sqrt 3 + 1}} + \frac{{2 - \sqrt 3 }}{{2 - \left( {\sqrt 3 - 1} \right)}}\\
= \frac{{2 + \sqrt 3 }}{{3 + \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{3 - \sqrt 3 }}\\
= \frac{{\left( {2 + \sqrt 3 } \right)\left( {3 - \sqrt 3 } \right) + \left( {2 - \sqrt 3 } \right)\left( {3 + \sqrt 3 } \right)}}{{\left( {3 + \sqrt 3 } \right)\left( {3 - \sqrt 3 } \right)}}\\
= \frac{{6 - 2\sqrt 3 + 3\sqrt 3 - 3 + 6 + 2\sqrt 3 - 3\sqrt 3 - 3}}{{9 - 3}}\\
= \frac{6}{6} = 1\\
b)B = \sqrt {6 + 2\sqrt 5 - \sqrt {29 - 12\sqrt 5 } } \\
= \sqrt {6 + 2\sqrt 5 - \sqrt {20 - 2.3.2\sqrt 5 + 9} } \\
= \sqrt {6 + 2\sqrt 5 - \sqrt {{{\left( {2\sqrt 5 - 3} \right)}^2}} } \\
= \sqrt {6 + 2\sqrt 5 - 2\sqrt 5 + 3} \\
= \sqrt {6 + 3} \\
= \sqrt 9 = 3\\
C = \sqrt 2 \left( {\sqrt 3 + 1} \right)\sqrt {2 - \sqrt 3 } \\
= \left( {\sqrt 3 + 1} \right)\sqrt {4 - 2\sqrt 3 } \\
= \left( {\sqrt 3 + 1} \right)\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
= \left( {\sqrt 3 + 1} \right)\left( {\sqrt 3 - 1} \right)\\
= 3 - 1\\
= 2
\end{array}$
