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Giải thích các bước giải:

\(1.\ 2\sqrt{3}.3\sqrt{6}=2.3.\sqrt{3.6}=6\sqrt{18}=6\sqrt{9.2}=18\sqrt{2}\\ 2.\ (-2\sqrt{2}).\sqrt{10}=-2\sqrt{2.10}=-2\sqrt{20}=-2\sqrt{4.5}=-2.2\sqrt{5}=-4\sqrt{5}\\ 3.\ (-7\sqrt{7}).(-2\sqrt{8})=(-7).(-2)\sqrt{7.8}=14\sqrt{56}=14\sqrt{4.14}=28\sqrt{14}\\ 4.\ 3\sqrt{3}.5\sqrt{6}=3.5\sqrt{3.6}=15\sqrt{18}=15\sqrt{9.2}=15.3\sqrt{2}=45\sqrt{2}\\ 5.\ -\sqrt{33}.3\sqrt{3}=-\sqrt{33}.\sqrt{9.3}=-\sqrt{33}.\sqrt{27}=-\sqrt{891}=-\sqrt{81.11}=-9\sqrt{11}\\ 6.\ 8\sqrt{6}.(-2\sqrt{24})=8.(-2)\sqrt{6.24}=-16\sqrt{144}=-16\sqrt{12.12}=-16\sqrt{12^{2}}=-192\\ 7.\ 9\sqrt{3}.3\sqrt{27}=9.3\sqrt{3.27}=27\sqrt{81}=27\sqrt{9^{2}}=27.9=243\\ 8.\ (3\sqrt{5}).(-10\sqrt{3})=3.(-10)\sqrt{5.3}=-30\sqrt{15}\\ 9.\ \dfrac{1}{2}\sqrt{5}.(-6\sqrt{2})=\dfrac{1}{2}.(-6)\sqrt{5.2}=-3\sqrt{10}\\ 10.\ \dfrac{2}{3}\sqrt{7}.\bigg(\dfrac{-9}{16}\sqrt{3}\bigg)=\dfrac{2}{3}.\dfrac{-9}{16}\sqrt{7.3}=\dfrac{-3}{8}\sqrt{21}=\dfrac{-3\sqrt{21}}{8}\\ 11.\ 15\sqrt{6}:5\sqrt{3}=15:5\sqrt{6:3}=3\sqrt{2}\\ 12.\ -25\sqrt{12}:(-5\sqrt{6})=(-25):(-5)\sqrt{12:6}=5\sqrt{2}\\ 13.\ 36\sqrt{8}:12\sqrt{2}=36:12\sqrt{8:2}=3\sqrt{4}=6\\ 14.\ 4\sqrt{27}:-2\sqrt{3}=4:(-2)\sqrt{27:3}=-2\sqrt{9}=-6\\ 15.\ 2\sqrt{48}:2\sqrt{3}=2:2\sqrt{48:3}=\sqrt{16}=4\\ 16.\ 5\sqrt{3}:\sqrt{15}=\sqrt{25.3}:\sqrt{15}=\sqrt{75}:\sqrt{15}=\sqrt{75:15}=\sqrt{5}\\ 17.\ -3\sqrt{5}:\sqrt{15}=-\sqrt{45}:\sqrt{15}=-\sqrt{45:15}=-\sqrt{3}\\ 18.\ 7\sqrt{5}:\sqrt{35}=\sqrt{49.5}:\sqrt{35}=\sqrt{245}:\sqrt{35}=\sqrt{245:35}=\sqrt{7}\\ 19.\ 5\sqrt{7}:(-\sqrt{35})=\sqrt{25.7}:(-\sqrt{35})=\sqrt{175}:(-\sqrt{35})=-\sqrt{175:35}=-\sqrt{5}\\ 20.\ 6\sqrt{5}:\sqrt{30}=\sqrt{36.5}:\sqrt{30}=\sqrt{180}:\sqrt{30}=\sqrt{180:30}=\sqrt{6}\)

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