a: \(-\dfrac{1}{2}\sqrt{12}+\dfrac{2}{3}\cdot\sqrt{48}+\dfrac{1}{15}\cdot\sqrt{75}-\dfrac{4}{3}\cdot\sqrt{162}\)
\(=-\dfrac{1}{2}\cdot2\sqrt{3}+\dfrac{2}{3}\cdot4\sqrt{3}+\dfrac{1}{15}\cdot5\sqrt{3}-\dfrac{4}{3}\cdot9\sqrt{2}\)
\(=-\sqrt{3}+\dfrac{8}{3}\sqrt{3}+\dfrac{1}{3}\sqrt{3}-12\sqrt{2}\)
\(=2\sqrt{3}-12\sqrt{2}\)
b: \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right)\cdot\sqrt{17-12\sqrt{2}}\)
\(=\left(\dfrac{\sqrt{5}\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}+\dfrac{14\left(2\sqrt{2}+1\right)}{8-1}-\dfrac{6\left(2+\sqrt{2}\right)}{4-2}\right)\cdot\sqrt{\left(3-2\sqrt{2}\right)^2}\)
\(=\left(\sqrt{5}\left(\sqrt{2}-1\right)+2\left(2\sqrt{2}+1\right)-3\left(2+\sqrt{2}\right)\right)\cdot\left(3-2\sqrt{2}\right)\)
\(=\left(\sqrt{10}-\sqrt{5}+4\sqrt{2}+2-6-3\sqrt{2}\right)\left(3-2\sqrt{2}\right)\)
\(=\left(\sqrt{10}-\sqrt{5}+\sqrt{2}-4\right)\left(3-2\sqrt{2}\right)\)
\(=3\sqrt{10}-2\sqrt{20}-3\sqrt{5}+2\sqrt{10}+3\sqrt{2}-4-12+8\sqrt{2}\)
\(=5\sqrt{10}-4\sqrt{5}-3\sqrt{5}+11\sqrt{2}-16\)
\(=5\sqrt{10}-7\sqrt{5}+11\sqrt{2}-16\)
