Đáp án:
\(\begin{array}{l}
a)6 - 2\sqrt 3 \\
b)8\sqrt 5 - 16\\
c)2\sqrt {10} - 2\sqrt 3 \\
d)\dfrac{{ - 217 + 9\sqrt {33} }}{{ - 347}}\\
e)\dfrac{{18 + 5\sqrt {10} }}{2}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{12}}{{3 - \sqrt 3 }} = \dfrac{{12\left( {3 - \sqrt 3 } \right)}}{{9 - 3}}\\
= 2\left( {3 - \sqrt 3 } \right)\\
= 6 - 2\sqrt 3 \\
b)\dfrac{8}{{\sqrt 5 + 2}} = \dfrac{{8\left( {\sqrt 5 - 2} \right)}}{{5 - 4}}\\
= 8\sqrt 5 - 16\\
c)\dfrac{{14\left( {\sqrt {10} - \sqrt 3 } \right)}}{{10 - 3}} = 2\left( {\sqrt {10} - \sqrt 3 } \right)\\
= 2\sqrt {10} - 2\sqrt 3 \\
d)\dfrac{{\left( {7\sqrt 3 - 5\sqrt {11} } \right)\left( {8\sqrt 3 + 7\sqrt {11} } \right)}}{{\left( {8\sqrt 3 + 7\sqrt {11} } \right)\left( {8\sqrt 3 - 7\sqrt {11} } \right)}}\\
= \dfrac{{56.3 + 49\sqrt {33} - 40\sqrt {33} - 7.5.11}}{{192 - 539}}\\
= \dfrac{{ - 217 + 9\sqrt {33} }}{{ - 347}}\\
e)\dfrac{{\left( {3\sqrt 5 - 2\sqrt 2 } \right)\left( {2\sqrt 5 + 3\sqrt 2 } \right)}}{{\left( {2\sqrt 5 + 3\sqrt 2 } \right)\left( {2\sqrt 5 - 3\sqrt 2 } \right)}}\\
= \dfrac{{6.5 + 9.\sqrt {10} - 2.2\sqrt {10} - 6.2}}{{4.5 - 9.2}}\\
= \dfrac{{18 + 5\sqrt {10} }}{2}
\end{array}\)
