a: \(20\sqrt{\dfrac{1}{5}}-3\sqrt{20}+\dfrac{4}{\sqrt{5}-\sqrt{3}}\)
\(=\dfrac{20}{\sqrt{5}}-3\cdot2\sqrt{5}+\dfrac{4\left(\sqrt{5}+\sqrt{3}\right)}{5-3}\)
\(=4\sqrt{5}-6\sqrt{5}+2\left(\sqrt{5}+\sqrt{3}\right)\)
\(=-2\sqrt{5}+2\sqrt{5}+2\sqrt{3}=2\sqrt{3}\)
b: \(\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{14+6\sqrt{5}}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(3+\sqrt{5}\right)^2}\)
\(=\left|\sqrt{5}-2\right|-\left|3+\sqrt{5}\right|\)
\(=\sqrt{5}-2-3-\sqrt{5}=-5\)
c: \(\dfrac{2\sqrt{3}-3\sqrt{2}}{\sqrt{6}}-\dfrac{2-\sqrt{2}}{1-\sqrt{2}}+\dfrac{3}{\sqrt{3}}\)
\(=\dfrac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\sqrt{6}}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}+\sqrt{3}\)
\(=\sqrt{2}-\sqrt{3}+\sqrt{3}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\)
\(=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
