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\(2\sqrt{3a}-\sqrt{75a}+a\sqrt{\frac{6}{5}.\frac{5}{2a}}-\frac{2}{5}\sqrt{300a^3}\)
\(=2\sqrt{3a}-5\sqrt{3a}+a\sqrt{\frac{3}{2}}-\frac{2}{5}.10.a\sqrt{3a}\)
\(=-3\sqrt{3a}+\sqrt{\frac{3}{a}.a^2-4\sqrt{3a}}\)
\(=-3\sqrt{3a}+\sqrt{3a}-4a\sqrt{3a}\)
\(=-2\sqrt{3a}-4a\sqrt{3a}\)
\(=-2\sqrt{3a}\left(1+2a\right)\)
a: \(=-10\sqrt{2}+10-\left(18-2\cdot3\sqrt{2}\cdot5+25\right)\)
\(=-10\sqrt{2}+19-43+30\sqrt{2}\)
\(=-24+20\sqrt{2}\)
b: \(=2\sqrt{3a}-5\sqrt{3a}+a\cdot\sqrt{\dfrac{27}{4a}}-\dfrac{2}{5}\cdot10a\sqrt{3a}\)
\(=-3\sqrt{3a}-4a\sqrt{3a}+\sqrt{\dfrac{27a}{4}}\)
\(=-3\sqrt{3a}-4a\sqrt{3a}+\dfrac{3}{2}\sqrt{3a}\)
\(=\sqrt{3a}\left(-\dfrac{3}{2}-4a\right)\)
\(2\sqrt{3a}-\sqrt{75a}+a\sqrt{\dfrac{13,5}{2a}}-\dfrac{2}{5}\sqrt{300a^2}\)
\(=2\sqrt{3a}-5\sqrt{3a}+a\sqrt{\dfrac{27a}{\left(2a\right)^2}}-\dfrac{2}{5}\sqrt{100a^2.300}\\ =2\sqrt{a}-5\sqrt{3a}+\dfrac{a.3}{2a}\sqrt{3a}-\dfrac{2}{5}\left|10a\right|\sqrt{3a}\\ =2\sqrt{3a}-5\sqrt{3a}+1,5\sqrt{3a}-4a\sqrt{3a}\\ =-1,5\sqrt{3a}-4a\sqrt{3a}\)
\(=2\sqrt{3a}-5\sqrt{3a}+\dfrac{3}{2}\sqrt{3a}-10\sqrt{3a}\)
\(=-\dfrac{23}{2}\sqrt{3a}\)
a) \(\left(2-\sqrt{2}\right)\left(-5\sqrt{2}\right)-\left(3\sqrt{2}-5\right)^2\)
\(=-10\sqrt{2}+5.2-\left(18-30\sqrt{2}+25\right)\)
\(=-10\sqrt{2}+10-18+30\sqrt{2}-25\)
\(=20\sqrt{2}-33\)
b) câu b đề sai
