Đáp án:
$\begin{array}{l}
a)\sqrt {20} + 2\sqrt {45} - 15\dfrac{{\sqrt 5 }}{5}\\
= 2\sqrt 5 + 2.3\sqrt 5 - 3\sqrt 5 \\
= 5\sqrt 5 \\
b)\dfrac{{\sqrt {35} - \sqrt 7 }}{{\sqrt 5 - 1}} + \dfrac{{12}}{{\sqrt 7 - 1}}\\
= \dfrac{{\sqrt 7 \left( {\sqrt 5 - 1} \right)}}{{\sqrt 5 - 1}} + \dfrac{{12\left( {\sqrt 7 + 1} \right)}}{{7 - 1}}\\
= \sqrt 7 + 2.\left( {\sqrt 7 + 1} \right)\\
= 3\sqrt 7 + 2\\
c)\sqrt {8 + 2\sqrt 7 } - \sqrt {28} \\
= \sqrt {7 + 2\sqrt 7 .1 + 1} - \sqrt {4.7} \\
= \sqrt {{{\left( {\sqrt 7 + 1} \right)}^2}} - 2\sqrt 7 \\
= \sqrt 7 + 1 - 2\sqrt 7 \\
= 1 - \sqrt 7 \\
d)3 - \sqrt 6 - \sqrt {{{\left( {\sqrt 6 - 2} \right)}^2}} + 6.\dfrac{{\sqrt 6 }}{3}\\
= 3 - \sqrt 6 - \left( {\sqrt 6 - 2} \right) + 2\sqrt 6 \\
= 3 - \sqrt 6 - \sqrt 6 + 2 + 2\sqrt 6 \\
= 5
\end{array}$
