Đáp án:

\(\begin{array}{l}
\dfrac{1}{{3\sqrt 3 }} = \dfrac{{\sqrt 3 }}{9}\\
\dfrac{5}{{2\sqrt 5 }} = \dfrac{{\sqrt 5 }}{2}\\
\dfrac{{2\sqrt 2  + 2}}{{5\sqrt 2 }} = \dfrac{{2 + \sqrt 2 }}{5}\\
\dfrac{2}{{\sqrt 3  - 1}} = \sqrt 3  + 1\\
\dfrac{{26}}{{5 - 2\sqrt 3 }} = 10 + 4\sqrt 3 \\
\dfrac{{\sqrt 5  - \sqrt 3 }}{{\sqrt 2 }} = \dfrac{{\sqrt {10}  - \sqrt 6 }}{2}
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
\dfrac{1}{{3\sqrt 3 }} = \dfrac{{\sqrt 3 }}{{3.{{\sqrt 3 }^2}}} = \dfrac{{\sqrt 3 }}{{3.3}} = \dfrac{{\sqrt 3 }}{9}\\
\dfrac{5}{{2\sqrt 5 }} = \dfrac{{{{\sqrt 5 }^2}}}{{2\sqrt 5 }} = \dfrac{{\sqrt 5 }}{2}\\
\dfrac{{2\sqrt 2  + 2}}{{5\sqrt 2 }} = \dfrac{{2\sqrt 2  + {{\sqrt 2 }^2}}}{{5\sqrt 2 }} = \dfrac{{\sqrt 2 .\left( {2 + \sqrt 2 } \right)}}{{5\sqrt 2 }} = \dfrac{{2 + \sqrt 2 }}{5}\\
\dfrac{2}{{\sqrt 3  - 1}} = \dfrac{{2.\left( {\sqrt 3  + 1} \right)}}{{\left( {\sqrt 3  - 1} \right)\left( {\sqrt 3  + 1} \right)}} = \dfrac{{2.\left( {\sqrt 3  + 1} \right)}}{{{{\sqrt 3 }^2} - {1^2}}} = \dfrac{{2.\left( {\sqrt 3  + 1} \right)}}{2} = \sqrt 3  + 1\\
\dfrac{{26}}{{5 - 2\sqrt 3 }} = \dfrac{{26\left( {5 + 2\sqrt 3 } \right)}}{{\left( {5 - 2\sqrt 3 } \right)\left( {5 + 2\sqrt 3 } \right)}} = \dfrac{{26\left( {5 + 2\sqrt 3 } \right)}}{{{5^2} - {{\left( {2\sqrt 3 } \right)}^2}}}\\
 = \dfrac{{26.\left( {5 + 2\sqrt 3 } \right)}}{{25 - 12}} = \dfrac{{26.\left( {5 + 2\sqrt 3 } \right)}}{{13}} = 2.\left( {5 + 2\sqrt 3 } \right) = 10 + 4\sqrt 3 \\
\dfrac{{\sqrt 5  - \sqrt 3 }}{{\sqrt 2 }} = \dfrac{{\sqrt 2 .\left( {\sqrt 5  - \sqrt 3 } \right)}}{{{{\sqrt 2 }^2}}} = \dfrac{{\sqrt {10}  - \sqrt 6 }}{2}
\end{array}\)

Đáp án+giải thích các bước giải:

B1:

`\frac{1}{3\sqrt{3}}=\frac{1.\sqrt{3}}{3.\sqrt{3}.\sqrt{3}}=\frac{\sqrt{3}}{9}`

`\frac{5}{2\sqrt{5}=\frac{5.\sqrt{5}}{2.\sqrt{5}.\sqrt{5}}`=\frac{5\sqrt{5}}{10}`

`\frac{2\sqrt{2}+2}{5\sqrt{2}}=\frac{4+2\sqrt{2}}{10}`

`\frac{2}{\sqrt{3}-1}=\frac{2(\sqrt{3}+1)}{3-1}=\frac{2(\sqrt{3}+1}{2}=\frac{\sqrt{3}+1}`

`\frac{26}{5-2\sqrt{3}}=\frac{26(5+2\sqrt{3})}{25-12}=\frac{26(\5+2\sqrt{3}{13}=10+4\sqrt{3}`

`\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{2}.(\sqrt{5}-\sqrt{3})}{2}=\frac{\sqrt{10}-\sqrt{6}}{2}`