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\(0,5\sqrt{100}-\sqrt{\frac{4}{25}}=0,5.10-\frac{\sqrt{4}}{\sqrt{25}}=5-\frac{2}{5}=\frac{23}{5}=\frac{138}{30}\)
\(\left(\sqrt{1\frac{1}{9}-\sqrt{\frac{9}{16}}}\right):5=\left(\sqrt{\frac{10}{9}-\frac{3}{4}}\right):5=\sqrt{\frac{13}{36}}:5=\frac{\sqrt{13}}{6}:5=\frac{\sqrt{13}}{30}\)
Vì 13 < 138 nên \(\sqrt{13}< 138\Rightarrow\frac{\sqrt{13}}{30}< \frac{138}{30}\)
Vậy \(0,5\sqrt{100}-\sqrt{\frac{4}{25}}>\left(\sqrt{1\frac{1}{9}-\sqrt{\frac{9}{16}}}\right):5\).
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{\frac{9}{25}}+\sqrt{\frac{1}{6}}-\sqrt{\frac{4}{49}}\)\(=\sqrt{\left(\frac{3}{5}\right)^2}+\sqrt{\frac{1}{6}}-\sqrt{\left(\frac{2}{7}\right)^2}\)\(=\frac{3}{5}+\sqrt{\frac{1}{6}}-\frac{2}{7}\)\(=\left(\frac{3}{5}-\frac{2}{7}\right)+\sqrt{\frac{1}{6}}\)\(=\left(\frac{21}{35}-\frac{10}{35}\right)+\sqrt{\frac{1}{6}}\)\(=\frac{11}{35}+\sqrt{\frac{1}{6}}\)\(=\sqrt{\frac{1.6}{6.6}}+\frac{11}{35}\)\(=\frac{\sqrt{6}}{6}+\frac{11}{35}\)\(=\frac{35\sqrt{6}}{210}+\frac{66}{210}\)\(=\frac{35\sqrt{6}+66}{210}\)
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Bai 1
a) \(\sqrt{0,36}+\sqrt{0,49}=0,6+0,7=1,3\)
b) \(\sqrt{\frac{4}{9}}-\sqrt{\frac{25}{36}}=\frac{2}{3}-\frac{5}{6}\)
=\(-\frac{1}{6}\)
Bài 2
a)\(x^2=81\Rightarrow\left[{}\begin{matrix}x=9\\x=-9\end{matrix}\right.\)
b) \(\left(x-1\right)^2=\frac{9}{16}\)
\(\Rightarrow\left[{}\begin{matrix}x-1=\frac{3}{4}\\x-1=\frac{-3}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{7}{4}\\x=\frac{1}{4}\end{matrix}\right.\)
c) \(x-2\sqrt{x}=0\Rightarrow\sqrt{x}\left(\sqrt{x}-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
d) \(x=\sqrt{x}\Rightarrow x-\sqrt{x}=0\Rightarrow\sqrt{x}\left(\sqrt{x}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{\frac{1}{9}+\frac{1}{16}}\)
\(=\frac{1}{3}+\frac{1}{4}\)
\(=\frac{7}{12}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{1}{4}+\frac{1}{3}:2x=-5\)
\(\frac{1}{3}:2x=\frac{-21}{4}\)
\(2x=\frac{-4}{63}\)
\(x=\frac{2}{63}\)
b) \(\left(3x-\frac{1}{4}\right)\left(x+\frac{1}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{12}\\x=\frac{-1}{2}\end{cases}}\)
Vậy.........
cái chỗ 1/9 kia là mình tưởng nó bị lỗi, nên gõ thêm vào