Đáp án:
\(\begin{array}{l}
5)\dfrac{{14 - 5\sqrt 3 }}{{22}}\\
7) - 4\sqrt 6 \\
9) - 2\\
6)1\\
8)3\\
10)8
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
5)\left[ {\dfrac{{2\left( {\sqrt 3 + 1} \right)}}{{3 - 1}} + \dfrac{{3\left( {\sqrt 3 + 2} \right)}}{{3 - 4}} + \dfrac{{15\left( {3 + \sqrt 3 } \right)}}{{9 - 3}}} \right].\dfrac{1}{{\sqrt 3 + 5}}\\
= \left[ {\dfrac{{2\left( {\sqrt 3 + 1} \right)}}{2} - 3\left( {\sqrt 3 + 2} \right) + \dfrac{{5\left( {3 + \sqrt 3 } \right)}}{2}} \right].\dfrac{1}{{\sqrt 3 + 5}}\\
= \left( {\sqrt 3 + 1 - 3\sqrt 3 - 6 + \dfrac{{5\left( {3 + \sqrt 3 } \right)}}{2}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\
= \dfrac{{ - 6\sqrt 3 - 10 + 15 + 5\sqrt 3 }}{2}.\dfrac{1}{{\sqrt 3 + 5}}\\
= \dfrac{{ - \sqrt 3 + 5}}{2}.\dfrac{1}{{\sqrt 3 + 5}}\\
= \dfrac{{14 - 5\sqrt 3 }}{{22}}\\
7)\dfrac{{5 - 2\sqrt 6 - 5 - 2\sqrt 6 }}{{25 - 24}}\\
= - 4\sqrt 6 \\
9)\dfrac{{\sqrt 3 \left( {\sqrt 5 - 2} \right)}}{{\sqrt 5 - 2}} - \dfrac{{2 + \sqrt 3 }}{{4 - 3}}\\
= \sqrt 3 - 2 - \sqrt 3 = - 2\\
6)\dfrac{{\sqrt 2 - 1}}{{2 - 1}} + \dfrac{{\sqrt 3 - \sqrt 2 }}{{3 - 2}} + \dfrac{{\sqrt 4 - \sqrt 3 }}{{4 - 3}}\\
= \sqrt 2 - 1 + \sqrt 3 - \sqrt 2 + \sqrt 4 - \sqrt 3 \\
= - 1 + 2 = 1\\
8)\sqrt 3 + \dfrac{{2\sqrt 3 \left( {\sqrt 3 - 1} \right)}}{{3 - 1}}\\
= \sqrt 3 + 3 - \sqrt 3 = 3\\
10)\dfrac{{3 + 2\sqrt {15} + 5 + \left( {5 - 2\sqrt {15} + 3} \right)}}{{5 - 3}}\\
= \dfrac{{16}}{2} = 8
\end{array}\)
