a: \(2\sqrt{28}-\dfrac{2}{3}\cdot\sqrt{63}-3\sqrt{700}\)
\(=2\cdot2\sqrt{7}-\dfrac{2}{3}\cdot3\sqrt{7}-3\cdot10\sqrt{7}\)
\(=4\sqrt{7}-2\sqrt{7}-30\sqrt{7}=-28\sqrt{7}\)
b: \(\sqrt{\left(1+\sqrt{6}\right)^2}+\sqrt{\left(\sqrt{6}-2\right)^2}\)
\(=\left|1+\sqrt{6}\right|+\left|\sqrt{6}-2\right|\)
\(=1+\sqrt{6}+\sqrt{6}-2=2\sqrt{6}-1\)
c: \(\dfrac{\sqrt{3}+\sqrt{15}}{1+\sqrt{5}}-\dfrac{4}{\sqrt{3}-1}\)
\(=\dfrac{\sqrt{3}\left(1+\sqrt{5}\right)}{1+\sqrt{5}}-\dfrac{4\left(\sqrt{3}+1\right)}{3-1}\)
\(=\sqrt{3}-2\left(\sqrt{3}+1\right)\)
\(=\sqrt{3}-2\sqrt{3}-2=-\sqrt{3}-2\)
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