Đáp án:
c. 1
Giải thích các bước giải:
\(\begin{array}{l}
a.\dfrac{{\sqrt 2 + \sqrt 3 + \sqrt 6 + 2\sqrt 2 + 2}}{{\sqrt 2 + \sqrt 3 + 2}}\\
= \dfrac{{\left( {\sqrt 2 + \sqrt 3 + 2} \right) + \left( {\sqrt 6 + 2\sqrt 2 } \right)}}{{\sqrt 2 + \sqrt 3 + 2}}\\
= 1 + \dfrac{{\sqrt 6 + 2\sqrt 2 }}{{\sqrt 2 + \sqrt 3 + 2}}\\
b.\dfrac{{10.3\sqrt 2 + 5\sqrt 3 - 15.3\sqrt 3 }}{{\sqrt 3 \left( {\sqrt 6 - 4} \right)}}\\
= \dfrac{{30\sqrt 2 - 40\sqrt 3 }}{{\sqrt 3 \left( {\sqrt 6 - 4} \right)}}\\
= \dfrac{{10.\sqrt 3 .\sqrt 3 .\sqrt 2 - 40\sqrt 3 }}{{\sqrt 3 \left( {\sqrt 6 - 4} \right)}}\\
= \dfrac{{10\sqrt 6 - 40}}{{\sqrt 6 - 4}}\\
= \dfrac{{10\left( {\sqrt 6 - 4} \right)}}{{\sqrt 6 - 4}} = 10\\
c.\sqrt {2 + \sqrt 3 } .\sqrt {2 + \sqrt {2 + \sqrt 3 } } .\sqrt {2 + \sqrt {2 + \sqrt {2 + \sqrt 3 } } } .\sqrt {2 - \sqrt {2 + \sqrt {2 + \sqrt 3 } } } \\
= \sqrt {2 + \sqrt 3 } .\sqrt {2 + \sqrt {2 + \sqrt 3 } } .\sqrt {4 - {{\left( {\sqrt {2 + \sqrt {2 + \sqrt 3 } } } \right)}^2}} \\
= \sqrt {2 + \sqrt 3 } .\sqrt {2 + \sqrt {2 + \sqrt 3 } } .\sqrt {4 - \left( {2 + \sqrt {2 + \sqrt 3 } } \right)} \\
= \sqrt {2 + \sqrt 3 } .\sqrt {2 + \sqrt {2 + \sqrt 3 } } .\sqrt {2 - \sqrt {2 + \sqrt 3 } } \\
= \sqrt {2 + \sqrt 3 } .\sqrt {4 - {{\left( {\sqrt {2 + \sqrt 3 } } \right)}^2}} \\
= \sqrt {2 + \sqrt 3 } .\sqrt {4 - 2 - \sqrt 3 } \\
= \sqrt {2 + \sqrt 3 } .\sqrt {2 - \sqrt 3 } \\
= \sqrt {4 - 3} = 1
\end{array}\)
