\(a,2\sqrt{20}-\sqrt{45}+3\sqrt{18}+3\sqrt{32}-\sqrt{50}=2.\sqrt{2^2.5}-\sqrt{3^2.5}+3\sqrt{2.3^2}+3.\sqrt{4^2.2}-\sqrt{5^2.2}\\ =2.2\sqrt{5}-3\sqrt{5}+3.3\sqrt{2}+3.4\sqrt{2}\\ =4\sqrt{5}-3\sqrt{5}+9\sqrt{2}+12\sqrt{2}\\ =21\sqrt{2}+\sqrt{5}\)
\(b,\sqrt{32}+\sqrt{0,5}-2\sqrt{\dfrac{1}{3}}-\sqrt{\dfrac{1}{8}}+\sqrt{48}\\ =\sqrt{4^2.2}+\sqrt{2.\left(\dfrac{1}{2}\right)^2}-2\sqrt{3.\left(\dfrac{1}{3}\right)^2}+\sqrt{2.\left(\dfrac{1}{4}\right)^2}+\sqrt{4^2.3}\\ =4\sqrt{2}+\dfrac{1}{2}\sqrt{2}-\dfrac{2}{3}\sqrt{3}+\dfrac{1}{4}\sqrt{2}+4\sqrt{3}=\left(4\sqrt{2}+\dfrac{1}{2}\sqrt{2}+\dfrac{1}{4}\sqrt{2}\right)+\left(4\sqrt{3}-\dfrac{2}{3}\sqrt{3}\right)\\ =\dfrac{19}{4}\sqrt{2}+\dfrac{10}{3}\sqrt{3}\)
\(c,\sqrt{\dfrac{1}{2}}+\sqrt{4,5}-\sqrt{12,5}-0,5\sqrt{200}+\sqrt{242}+6\sqrt{1\dfrac{1}{8}}-\sqrt{24,5}\\ \\ =\sqrt{2.\left(\dfrac{1}{2}\right)^2}+\sqrt{\left(\dfrac{3}{2}\right)^2.2}-\sqrt{2.\left(\dfrac{5}{2}\right)^2}-0,5.\sqrt{2.10^2}+\sqrt{2.11^2}+6.\sqrt{2.\left(\dfrac{3}{4}\right)^2}-\sqrt{2.\left(\dfrac{7}{2}\right)^2}\\ =\dfrac{1}{2}\sqrt{2}+\dfrac{3}{2}\sqrt{2}-\dfrac{5}{2}\sqrt{2}-0,5.10.\sqrt{2}+11\sqrt{2}+6.\dfrac{3}{4}\sqrt{2}-\dfrac{7}{2}\sqrt{2}\\ =\left(\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}-5+11+\dfrac{9}{2}-\dfrac{7}{2}\right)\sqrt{2}=\dfrac{13}{2}\sqrt{2}=\dfrac{13}{\sqrt{2}}\)
