Tính giá trị biểu thức \(\left( {\frac{{10 + 2\sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} + \frac{{\sqrt {30} - \sqrt 6 }}{{\sqrt 5 - 1}}} \right):\frac{1}{{2\sqrt 5 - \sqrt 6 }}\)

* Hướng dẫn giải

Ta có:

\(\begin{array}{l} \left( {\frac{{10 + 2\sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} + \frac{{\sqrt {30} - \sqrt 6 }}{{\sqrt 5 - 1}}} \right):\frac{1}{{2\sqrt 5 - \sqrt 6 }}\\ = \left( {\frac{{\sqrt {100} - \sqrt {40} }}{{\sqrt 5 + \sqrt 2 }} + \frac{{\sqrt 5 .\sqrt 6 - \sqrt 5 }}{{\sqrt 5 - 1}}} \right):\frac{1}{{2\sqrt 5 - \sqrt 6 }}\\ = \left( {\frac{{\sqrt {20} \left( {\sqrt 5 + \sqrt 2 } \right)}}{{\sqrt 5 + \sqrt 2 }} + \frac{{\sqrt 6 .\left( {\sqrt 5 - 1} \right)}}{{\sqrt 5 - 1}}} \right):\frac{1}{{2\sqrt 5 - \sqrt 6 }}\\ = \left( {2\sqrt 5 + \sqrt 6 } \right)\left( {2\sqrt 5 - \sqrt 6 } \right) = {\left( {2\sqrt 5 } \right)^2} - {\left( {\sqrt 6 } \right)^2} = 20 - 6 = 14 \end{array}\)