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`2\sqrt3 (\sqrt27 + 2\sqrt48 -\sqrt75)`
`=2\sqrt3 (3\sqrt3 + 8\sqrt3 - 5\sqrt3)`
`=2\sqrt3 . 6\sqrt3`
`=36`
\(=12\sqrt{3}-2\cdot4\sqrt{3}+3\cdot2\sqrt{3}-5\sqrt{3}\)
\(=12\sqrt{3}-8\sqrt{3}+6\sqrt{3}-5\sqrt{3}\)
\(=5\sqrt{3}\)
Ta có: \(\sqrt{27}-2\sqrt{3}+2\sqrt{48}-3\sqrt{75}\)
\(=3\sqrt{3}-2\sqrt{3}+8\sqrt{3}-15\sqrt{3}\)
\(=-6\sqrt{3}\)
a: \(=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)
a,\(\sqrt{12}\)+ \(2\sqrt{27}\)+\(3\sqrt{75}\)-\(9\sqrt{48}\)
b, (\(2\sqrt{2}\) - \(\sqrt{3}\))\(^2\)
a: \(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
\(=2\sqrt{3}+6\sqrt{3}+15\sqrt{3}-36\sqrt{3}\)
\(=-14\sqrt{3}\)
b: \(\left(2\sqrt{2}-\sqrt{3}\right)^2=11-4\sqrt{6}\)
√163 ≈ 12.767 √127 ≈ 11.269 √475 ≈ 21.794
2√163 - 3√127 - 6√475 ≈ 2(12.767) - 3(11.269) - 6(21.794)
≈ 25.534 - 33.807 - 130.764
≈ -138.037
Vậy giá trị của biểu thức 2√163 - 3√127 - 6√475 là -138.037.
\(=2\cdot\dfrac{4}{\sqrt{3}}-3\cdot\dfrac{1}{3\sqrt{3}}-6\cdot\dfrac{2}{5\sqrt{3}}\)
\(=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}=\dfrac{7}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}\)
\(=\dfrac{1}{\sqrt{3}}\left(7-\dfrac{12}{5}\right)=\dfrac{23}{5\sqrt{3}}=\dfrac{23\sqrt{3}}{15}\)
\(=2\cdot\dfrac{4}{\sqrt{3}}-3\cdot\dfrac{1}{3\sqrt{3}}-6\cdot\dfrac{2}{3\sqrt{5}}\\ =\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{4}{\sqrt{5}}=\dfrac{7}{\sqrt{3}}-\dfrac{4\sqrt{5}}{5}\\ =\dfrac{7\sqrt{3}}{3}-\dfrac{4\sqrt{5}}{5}=\dfrac{35\sqrt{3}-12\sqrt{5}}{15}\)
\(=2\sqrt{3}+3\sqrt{3}-15\sqrt{3}=-10\sqrt{3}\)