Đáp án:
\(\dfrac{{3 + \sqrt 5 - \sqrt {10} - 3\sqrt 2 }}{{\sqrt 2 }}\)
Giải thích các bước giải:
\(\begin{array}{l}
g)\sqrt {2\left( {8 + 2\sqrt {15} } \right)} - \sqrt {2\left( {4 - 2\sqrt 3 } \right)} - \sqrt {3 - \sqrt 5 } - \dfrac{{\sqrt 2 \left( {\sqrt 5 + 3} \right)}}{{\sqrt 2 }}\\
= \sqrt {2\left( {5 + 2\sqrt 5 .\sqrt 3 + 3} \right)} - \sqrt {2\left( {3 - 2\sqrt 3 .1 + 1} \right)} - \dfrac{{\sqrt {6 - 2\sqrt 5 } }}{{\sqrt 2 }} - \sqrt 5 - 3\\
= \sqrt {2{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2}} - \sqrt {2{{\left( {\sqrt 3 - 1} \right)}^2}} - \dfrac{{\sqrt {5 - 2\sqrt 5 .1 + 1} }}{{\sqrt 2 }} - \sqrt 5 - 3\\
= \left( {\sqrt 5 + \sqrt 3 } \right)\sqrt 2 - \left( {\sqrt 3 - 1} \right)\sqrt 2 - \dfrac{{\sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} }}{{\sqrt 2 }} - \sqrt 5 - 3\\
= \sqrt {10} + \sqrt 6 - \sqrt 6 + \sqrt 2 - \dfrac{{\sqrt 5 - 1}}{{\sqrt 2 }} - \sqrt 5 - 3\\
= \dfrac{{2\sqrt 5 + 2 - \sqrt 5 + 1 - \sqrt {10} - 3\sqrt 2 }}{{\sqrt 2 }}\\
= \dfrac{{3 + \sqrt 5 - \sqrt {10} - 3\sqrt 2 }}{{\sqrt 2 }}
\end{array}\)
