Đáp án:
$\begin{array}{l}
a)\sqrt {\dfrac{{81}}{{100}} + \sqrt {1\dfrac{{31}}{{225}}} } \\
= \sqrt {\dfrac{{81}}{{100}} + \sqrt {\dfrac{{256}}{{225}}} } \\
= \sqrt {\dfrac{{81}}{{100}} + \dfrac{{16}}{{15}}} \\
= \sqrt {\dfrac{{563}}{{300}}} = \dfrac{{\sqrt {1689} }}{{30}}\\
b)\left( {\sqrt {3\dfrac{6}{{25}}} + \sqrt {4,41} } \right):\sqrt {1\dfrac{{69}}{{100}}} \\
= \left( {\sqrt {\dfrac{{81}}{{25}}} + \sqrt {\dfrac{{441}}{{100}}} } \right):\sqrt {\dfrac{{169}}{{100}}} \\
= \left( {\dfrac{9}{5} + \dfrac{{21}}{{10}}} \right):\dfrac{{13}}{{10}}\\
= \dfrac{{39}}{{10}}.\dfrac{{10}}{{13}}\\
= 3\\
c)\left( {\sqrt {6\dfrac{1}{4}} - \sqrt {3.0,27} } \right).\sqrt {\dfrac{1}{{25}}} \\
= \left( {\sqrt {\dfrac{{25}}{4}} - \sqrt {0,81} } \right).\dfrac{1}{5}\\
= \left( {\dfrac{5}{2} - 0,9} \right).\dfrac{1}{5}\\
= \dfrac{8}{5}.\dfrac{1}{5} = \dfrac{8}{{25}}\\
d)\sqrt {\dfrac{{196}}{{169}}} + \sqrt {\dfrac{{49}}{{64}}} - \sqrt {1\dfrac{{25}}{{144}}} \\
= \dfrac{{14}}{{13}} + \dfrac{7}{8} - \dfrac{{13}}{{12}}\\
= \dfrac{{271}}{{312}}
\end{array}$
