Đáp án:
\( - \sqrt 2 \)
Giải thích các bước giải:
\(\begin{array}{l}
\sqrt {\dfrac{{\left( {9 - 4\sqrt 3 } \right)\left( {6 - \sqrt 3 } \right)}}{{36 - 3}}} - \sqrt {\dfrac{{\left( {3 + 4\sqrt 3 } \right)\left( {5\sqrt 3 + 6} \right)}}{{75 - 36}}} \\
= \sqrt {\dfrac{{54 - 9\sqrt 3 - 24\sqrt 3 + 12}}{{33}}} - \sqrt {\dfrac{{15\sqrt 3 + 18 + 20.3 + 24\sqrt 3 }}{{39}}} \\
= \sqrt {\dfrac{{66 - 33\sqrt 3 }}{{33}}} - \sqrt {\dfrac{{78 + 39\sqrt 3 }}{{39}}} \\
= \sqrt {2 - \sqrt 3 } - \sqrt {2 + \sqrt 3 } \\
= \dfrac{{\sqrt {4 - 2\sqrt 3 } - \sqrt {4 + 2\sqrt 3 } }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {3 - 2\sqrt 3 .1 + 1} - \sqrt {3 + 2\sqrt 3 .1 + 1} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 3 - 1 - \sqrt 3 - 1}}{{\sqrt 2 }}\\
= - \dfrac{2}{{\sqrt 2 }} = - \sqrt 2
\end{array}\)
