Đáp án:
$\begin{array}{l}
A = \left( {4\sqrt 3 - 4} \right)\sqrt {3 + \sqrt {5 - \sqrt {13 + 2\sqrt {12} } } } \\
= \left( {4\sqrt 3 - 4} \right)\sqrt {3 + \sqrt {5 - \sqrt {{{\left( {\sqrt {12} + 1} \right)}^2}} } } \\
= 4.\left( {\sqrt 3 - 1} \right)\sqrt {3 + \sqrt {5 - \sqrt {12} - 1} } \\
= 4\left( {\sqrt 3 - 1} \right).\sqrt {3 + \sqrt {4 - 2.\sqrt 3 } } \\
= 4\left( {\sqrt 3 - 1} \right).\sqrt {3 + \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} } \\
= 4.\left( {\sqrt 3 - 1} \right).\sqrt {3 + \sqrt 3 - 1} \\
= 4.\left( {\sqrt 3 - 1} \right)\sqrt {2 + \sqrt 3 } \\
= 2\sqrt 2 .\left( {\sqrt 3 - 1} \right)\sqrt {4 + 2\sqrt 3 } \\
= 2\sqrt 2 .\left( {\sqrt 3 - 1} \right).\sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} \\
= 2\sqrt 2 .\left( {\sqrt 3 - 1} \right).\left( {\sqrt 3 + 1} \right)\\
= 2\sqrt 2 .\left( {3 - 1} \right)\\
= 4\sqrt 2 \\
\end{array}$
$\begin{array}{l}
B = \sqrt {9 + \sqrt {17} } - \sqrt {9 - \sqrt {17} } - \sqrt {12} \\
= \frac{1}{{\sqrt 2 }}.\left( {\sqrt {18 + 2\sqrt {17} } - \sqrt {18 - 2\sqrt {17} } - 2\sqrt 3 } \right)\\
= \frac{1}{{\sqrt 2 }}.\left( {\sqrt {{{\left( {\sqrt {17} + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt {17} - 1} \right)}^2}} - 2\sqrt 3 } \right)\\
= \frac{1}{{\sqrt 2 }}.\left( {\sqrt {17} + 1 - \sqrt {17} + 1 - 2\sqrt 3 } \right)\\
= \frac{1}{{\sqrt 2 }}\left( {2 - 2\sqrt 3 } \right)\\
= \sqrt 2 - \sqrt 2 .\sqrt 3 \\
= \sqrt 2 - \sqrt 6
\end{array}$
