Rút gọn biểu thức:
\(\sqrt[3]{3a}-6\sqrt[3]{\frac{a}{9}}+a\sqrt[3]{\frac{3}{a^2}}-\sqrt[3]{5\sqrt{5}}\)
(với a khác 0)
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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) \(\sqrt{9a^4}=\sqrt{\left(3a^2\right)^2}=\left|3a^2\right|=3a^2\)
b) \(2\sqrt{a^2}-5a=2\left|a\right|-5a=-2a-5a=-7a\)
c) \(\sqrt{16\left(1+4x+4x^2\right)}=\sqrt{\left[4\left(1+2x\right)\right]^2}=\left|4\left(1+2x\right)\right|=4\left(1+2x\right)\)
a) \(=5\left|a\right|+3a=5a+3a=8a\)
b) \(=3\left|a^2\right|+3a^2=3a^2+3a^2=6a^2\)
c) \(=5.2\left|a^3\right|-3a^3=-10a^3-3a^3=-13a^3\)
Mình ghi nhầm. \(x=\frac{\sqrt{4+2\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)nhé
\(\sqrt[3]{3a}-6\sqrt[3]{\frac{a}{9}}+a\sqrt[3]{\frac{3}{a^2}}-\sqrt[3]{5\sqrt{5}}=\sqrt[3]{3a}-2\sqrt[3]{\frac{3^3}{9}a}+\sqrt[3]{\frac{3a^3}{a^2}}-\sqrt[3]{\sqrt{5}^3}\)
\(=\sqrt[3]{3a}-2\sqrt[3]{3a}+\sqrt[3]{3a}+\sqrt{5}=\sqrt{5}\)