Lời giải chi tiết:

\(\begin{array}{l}A = \frac{{\left( {5 + 2\sqrt 6 } \right)\left( {49 - 20\sqrt 6 } \right)\sqrt {5 - 2\sqrt 6 } }}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{\sqrt {5 + 2\sqrt 6 } .\sqrt {5 + 2\sqrt 6 } .\sqrt {5 - 2\sqrt 6 } \left( {49 - 20\sqrt 6 } \right)}}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{\sqrt {{{\sqrt 3 }^2} + 2\sqrt 3 .\sqrt 2  + {{\sqrt 2 }^2}} .\sqrt {\left( {5 + 2\sqrt 6 } \right)\left( {5 - 2\sqrt 6 } \right)} \left( {49 - 20\sqrt 6 } \right)}}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{\sqrt {{{\left( {\sqrt 3  + \sqrt 2 } \right)}^2}} .1.\left( {49 - 20\sqrt 6 } \right)}}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{\left( {\sqrt 3  + \sqrt 2 } \right).\left( {49 - 20\sqrt 6 } \right)}}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{49\sqrt 3  - 60\sqrt 2  + 49\sqrt 2  - 40\sqrt 3 }}{{9\sqrt 3  - 11\sqrt 2 }}\\ = \frac{{9\sqrt 3  - 11\sqrt 2 }}{{9\sqrt 3  - 11\sqrt 2 }}\\ = 1\end{array}\)