1) $(\sqrt{45}-\sqrt{20}+\sqrt{5}):\sqrt{6}$
$=(\sqrt{3^2.5}-\sqrt{2^2.5}+\sqrt{5}):\sqrt{6}$
$=(3\sqrt{5}-2\sqrt{5}+\sqrt{5}):\sqrt{6}$
$=6\sqrt{5}:\sqrt{6}$
$=\sqrt{6}.\sqrt{5}$
$=\sqrt{30}$
2) $\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}$
$=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{(3+\sqrt{2})(3-\sqrt{2})}$
$=\dfrac{6}{9-2}$
$=\dfrac{6}{7}$
3) $\sqrt{3}(\sqrt{12}+\sqrt{27}-\sqrt{3})$
$=\sqrt{3}(\sqrt{2^2.3}+\sqrt{3^2.3}-\sqrt{3})$
$=\sqrt{3}(2\sqrt{3}+3\sqrt{3}-\sqrt{3})$
$=\sqrt{3}.4\sqrt{3}$
$=3.4$
$=12$
4) $\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}$
$=\sqrt{2^2.5}-\sqrt{3^2.5}+3\sqrt{3^2.2}+\sqrt{6^2.2}$
$=2\sqrt{5}-3\sqrt{5}+3.3\sqrt{2}+6\sqrt{2}$
$=-\sqrt{5}+9\sqrt{2}+6\sqrt{2}$
$=-\sqrt{5}+15\sqrt{2}$
5) $\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}$
$=\sqrt{(3+\sqrt{5})(3-\sqrt{5})}$
$=\sqrt{9-5}$
$=\sqrt{4}$
$=2$
6) $2\sqrt{75}+\sqrt{48}-5\sqrt{300}$
$=2\sqrt{5^2.3}+\sqrt{4^2.3}-5\sqrt{10^2.3}$
$=2.5\sqrt{3}+4\sqrt{3}-5.10\sqrt{3}$
$=10\sqrt{3}+4\sqrt{3}-50\sqrt{3}$
$=-36\sqrt{3}$
7) $\sqrt{250}.\sqrt{\dfrac{16}{10}}$
$=\sqrt{250.\dfrac{16}{10}}$
$=\sqrt{400}$
$=20$
8) $(3\sqrt{5}-\sqrt{20}):\sqrt{5}$
$=(3\sqrt{5}-2\sqrt{5}):\sqrt{5}$
$=\sqrt{5}:\sqrt{5}$
$=1$
9) $\dfrac{\sqrt{24}-\sqrt{6}}{\sqrt{6}}$
$=\dfrac{\sqrt{2^2.6}-\sqrt{6}}{\sqrt{6}}$
$=\dfrac{2\sqrt{6}-\sqrt{6}}{\sqrt{6}}$
$=\dfrac{\sqrt{6}}{\sqrt{6}}$
$=1$
10) $\sqrt{50}-\dfrac{4}{3}.\sqrt{18}+\sqrt{32}$
$=\sqrt{5^2.2}-\dfrac{4}{3}.\sqrt{3^2.2}+\sqrt{4^2.2}$
$=5\sqrt{2}-\dfrac{4}{3}.3\sqrt{2}+4\sqrt{2}$
$=5\sqrt{2}-4\sqrt{2}+4\sqrt{2}$
$=5\sqrt{2}$
