Giải thích các bước giải:
\(\begin{array}{l}
1)\frac{{\sqrt {3.5} - \sqrt {3.2} }}{{ - \left( {\sqrt 5 - \sqrt 2 } \right)}} = \frac{{\sqrt 3 \left( {\sqrt 5 - \sqrt 2 } \right)}}{{ - \left( {\sqrt 5 - \sqrt 2 } \right)}}\\
= - \sqrt 3 \\
2)\sqrt {\frac{3}{{4.5}}} + \frac{1}{{2\sqrt {3.5} }} - \frac{2}{{\sqrt {3.5} }}\\
= \frac{1}{{\sqrt 5 }}\left( {\frac{{\sqrt 3 }}{2} + \frac{1}{{2\sqrt 3 }} - \frac{2}{{\sqrt 3 }}} \right)\\
= \frac{1}{{\sqrt 5 }}.\left( {\frac{{3 + 1 - 4}}{{2\sqrt 3 }}} \right)\\
= \frac{1}{{\sqrt 5 }}.0 = 0\\
3)\frac{{3\sqrt 5 + 3\sqrt 2 }}{3} + \frac{{4\sqrt 6 - 4\sqrt 2 }}{4}\\
= \frac{{12\sqrt 5 + 12\sqrt 2 + 12\sqrt 6 - 12\sqrt 2 }}{{12}}\\
= \sqrt 5 + \sqrt 6 \\
4)\left( {\frac{{\sqrt 5 + \sqrt 3 + \sqrt 5 - \sqrt 3 }}{2}} \right).\sqrt 5 \\
= \frac{{2\sqrt 5 .\sqrt 5 }}{2} = 5\\
5)\left( {\sqrt 5 + \sqrt 5 - \frac{5}{4}\sqrt {\frac{{4 + 5\sqrt 5 }}{5}} } \right).\frac{1}{{2\sqrt 5 }}\\
= \left( {2\sqrt 5 - \sqrt {\frac{{25.\left( {4 + 5\sqrt 5 } \right)}}{{16.5}}} } \right).\frac{1}{{2\sqrt 5 }}\\
= \left( {2\sqrt 5 - \sqrt {\frac{{20 + 25\sqrt 5 }}{{16}}} } \right).\frac{1}{{2\sqrt 5 }}\\
= \frac{{8\sqrt 5 - \sqrt {20 + 25\sqrt 5 } }}{4}.\frac{1}{{2\sqrt 5 }}\\
= \frac{{8\sqrt 5 - \sqrt {20 + 25\sqrt 5 } }}{{8\sqrt 5 }} = 1 - \frac{{\sqrt {4 + 25} }}{8}\\
6)\frac{1}{3}.4\sqrt 3 + 3.5\sqrt 3 - 3\sqrt 3 - 10.\frac{{2\sqrt 3 }}{3}\\
= \sqrt 3 .\frac{{20}}{3} = \frac{{20\sqrt 3 }}{3}
\end{array}\)
