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1) \(3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}\)
\(=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}\)
\(=-6\sqrt{2}\)
2) \(\sqrt{50}-\sqrt{18}+\sqrt{200}-\sqrt{162}\)
\(=5\sqrt{2}-3\sqrt{2}+10\sqrt{2}-9\sqrt{2}\)
\(=3\sqrt{2}\)
3) \(5\sqrt{5}+\sqrt{20}-3\sqrt{45}\)
\(=5\sqrt{5}+2\sqrt{5}-9\sqrt{5}\)
\(=-2\sqrt{5}\)
4) \(5\sqrt{48}-4\sqrt{27}-2\sqrt{75}+\sqrt{108}\)
\(=20\sqrt{3}-12\sqrt{3}-10\sqrt{3}+6\sqrt{3}\)
\(=4\sqrt{3}\)
5) \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{10}{3}\sqrt{3}\)
\(=-\dfrac{17}{3}\sqrt{3}\)
6: \(=3\cdot2\sqrt{3}-4\cdot3\sqrt{3}+5\cdot4\sqrt{3}=14\sqrt{3}\)
7: \(=2\sqrt{3}+5\sqrt{3}-4\sqrt{3}=3\sqrt{3}\)
8: \(=2\cdot4\sqrt{2}+4\cdot2\sqrt{2}-5\cdot3\sqrt{2}=\sqrt{2}\)
9: \(=3\cdot2\sqrt{5}-2\cdot3\sqrt{5}+4\sqrt{5}=4\sqrt{5}\)
10: \(=2\cdot2\sqrt{6}-2\cdot3\sqrt{6}+3\sqrt{6}-5\sqrt{6}=-4\sqrt{6}\)
\(\sqrt{27}-3\sqrt{48}+2\sqrt{108}-\sqrt{2-\sqrt{3}}^2=3\sqrt{3}-12\sqrt{3}+12\sqrt{3}-2+\sqrt{3}=3\sqrt{3}-2+\sqrt{3}=4\sqrt{3}-2=2\left(2\sqrt{3}-1\right)\)
Ta có: \(\sqrt{27}-3\sqrt{48}+2\sqrt{108}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=3\sqrt{3}-12\sqrt{3}+12\sqrt{3}-2+\sqrt{3}\)
\(=2\sqrt{3}-2\)
\(2\sqrt{3}\left(\sqrt{12}-\sqrt{27}-3\sqrt{2}\right)+6\sqrt{6}\)
\(=2\sqrt{3}\left(\sqrt{3.2^2}-\sqrt{3.3^2}-3\sqrt{2}\right)+6\sqrt{6}\)
\(=2\sqrt{3}\left(2\sqrt{3}-3\sqrt{3}-3\sqrt{2}\right)+6\sqrt{6}\)
\(=\left(2\sqrt{3}\right)^2-6.\left(\sqrt{3}\right)^2-6\sqrt{6}+6\sqrt{6}\)
\(=-6\)
a, (\(\sqrt{128}\)-\(\sqrt{50}\)+\(\sqrt{98}\)):\(\sqrt{2}\)
=(8-5+3)
=10
b, (\(\sqrt{48}\)+\(\sqrt{27}\)-\(\sqrt{192}\)):2\(\sqrt{3}\)
=(2+1,5-4)
=-0,5
c, \(\dfrac{1}{8}\)-3\(\sqrt{2}\) +\(\dfrac{1}{8}\)+3\(\sqrt{2}\)
=\(\dfrac{1}{4}\)
d, \(\sqrt{\left(1-\sqrt{5}\right)^2}-\sqrt{5}\)
=-1
d: Ta có: \(\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}\)
\(=\dfrac{\sqrt{12+2\sqrt{11}}-\sqrt{12-2\sqrt{11}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{11}+1-\sqrt{11}+1}{\sqrt{2}}\)
\(=\sqrt{2}\)
\(\dfrac{2}{\sqrt{3}-11}-\sqrt{27}+\dfrac{3}{\sqrt{3}}\)
\(=\dfrac{2\left(\sqrt{3}+11\right)}{3-121}-3\sqrt{3}+\sqrt{3}\)
\(=\dfrac{-1}{59}\left(11+\sqrt{3}\right)-2\sqrt{3}\)
\(=-\dfrac{11}{59}-\dfrac{\sqrt{3}}{59}-2\sqrt{3}=-\dfrac{11}{59}-\dfrac{119}{59}\sqrt{3}\)