Đáp án:
$\begin{array}{l}
\dfrac{{\sqrt {2 - \sqrt 3 } + \sqrt {4 - \sqrt {15} } + \sqrt {10} }}{{\sqrt {23 - 3\sqrt 5 } }}\\
= \dfrac{{\sqrt 2 .\left( {\sqrt {2 - \sqrt 3 } + \sqrt {4 - \sqrt {15} } + \sqrt {10} } \right)}}{{\sqrt 2 .\sqrt {23 - 3\sqrt 5 } }}\\
= \dfrac{{\sqrt {4 - 2\sqrt 3 } + \sqrt {8 - 2\sqrt {15} } + \sqrt {20} }}{{\sqrt {46 - 2.3\sqrt 5 } }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} + 2\sqrt 5 }}{{\sqrt {{{\left( {3\sqrt 5 - 1} \right)}^2}} }}\\
= \dfrac{{\sqrt 3 - 1 + \sqrt 5 - \sqrt 3 + 2\sqrt 5 }}{{3\sqrt 5 - 1}}\\
= \dfrac{{3\sqrt 5 - 1}}{{3\sqrt 5 - 1}}\\
= 1
\end{array}$
