Đáp án:
\(\begin{array}{l}
A = \sqrt 3 \\
B = - 9\\
C = 3\sqrt 2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = 5\sqrt 3 - 3\sqrt {48} + 2\sqrt {75} - \dfrac{1}{3}.\sqrt {108} \\
= 5\sqrt 3 - 3.4\sqrt 3 + 2.5\sqrt 3 - \dfrac{1}{3}.6\sqrt 3 \\
= \left( {5 - 12 + 10 - 2} \right)\sqrt 3 \\
= \sqrt 3 \\
B = \dfrac{{15}}{{\sqrt 6 + 1}} - \dfrac{6}{{\sqrt 6 - 2}}\\
= \dfrac{{15\left( {\sqrt 6 - 1} \right)}}{{6 - 1}} - \dfrac{{6\left( {\sqrt 6 + 2} \right)}}{{6 - 4}}\\
= 3\left( {\sqrt 6 - 1} \right) - 3\left( {\sqrt 6 + 2} \right)\\
= 3\sqrt 6 - 3 - 3\sqrt 6 - 6\\
= - 9\\
C = \sqrt {11 + 4\sqrt 6 } - \sqrt {5 - 2\sqrt 6 } \\
= \sqrt {8 + 2.2\sqrt 2 .\sqrt 3 + 3} - \sqrt {3 - 2\sqrt 3 .\sqrt 2 + 2} \\
= \sqrt {{{\left( {2\sqrt 2 + \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {\sqrt 3 - \sqrt 2 } \right)}^2}} \\
= 2\sqrt 2 + \sqrt 3 - \left( {\sqrt 3 - \sqrt 2 } \right)\\
= 2\sqrt 2 + \sqrt 3 - \sqrt 3 + \sqrt 2 \\
= 3\sqrt 2
\end{array}\)
