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\(a,\sqrt{81}=9\)
\(b.\sqrt{8100}=90\)
\(c,\sqrt{64}=8\)
\(d,\sqrt{25}=5\)
\(e,\sqrt{0,64}=0,8\)
\(f,\sqrt{10000}=100\)
\(g,\sqrt{0,01}=0,1\)
\(h,\sqrt{\frac{49}{100}}=\frac{7}{10}\)
\(i,\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}\)
\(j,\sqrt{\frac{4}{25}}=\frac{2}{5}\)
~Study well~
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a) 9
b) 90
c) 8
d) 5
e) 0,8
f) 100
g) 0,1
h) \(\frac{7}{10}\)
i) \(\frac{0,3}{11}\)
j) 0,4.
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{2}{3}\sqrt{81}-\left(\frac{-3}{4}\right):\sqrt{\frac{9}{64}}-\left(\frac{\sqrt{5}}{2011}\right)^0\)
\(=\frac{2}{3}\cdot9+\frac{3}{4}\cdot\frac{8}{3}-1\)
\(=6+2-1\)
\(=7\)
\(\frac{2}{3}\sqrt{81}-\left(-\frac{3}{4}\right):\sqrt{\frac{9}{64}}-\left(\frac{\sqrt{5}}{2011}\right)^0=\frac{2}{3}.9-\left(-2\right)-1=6+2-1=7\)
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a) \(A=\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}=\left(-1\right)^{3n+1}\)
b) \(B=\left(10000-1^2\right)\left(10000-2^2\right).........\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right)......\left(10000-100^2\right)....\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right).....\left(10000-10000\right).....\left(10000-1000^2\right)=0\)
c) \(C=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)..........\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right).....\left(\frac{1}{125}-\frac{1}{5^3}\right)......\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)........\left(\frac{1}{125}-\frac{1}{125}\right).....\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
d) \(D=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-10^3\right)}\)
\(=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-1000\right)}=1999^0=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=2014+\frac{2014}{1+2}+\frac{2014}{1+2+3}+...+\frac{2014}{1+2+3+...+10000}\)
\(S=\frac{2014}{\frac{1.2}{2}}+\frac{2014}{\frac{2.3}{2}}+\frac{2014}{\frac{3.4}{2}}+...+\frac{2014}{\frac{10000.10001}{2}}\)
\(S=\frac{4028}{1.2}+\frac{4028}{2.3}+\frac{4028}{3.4}+...+\frac{4028}{10000.10001}\)
\(S=4028\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10000.10001}\right)\)
\(S=4028\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{10001-10000}{10000.10001}\right)\)
\(S=4028\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10000}-\frac{1}{10001}\right)\)
\(S=4028\left(1-\frac{1}{10001}\right)=\frac{40280000}{10001}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{9999}{10000}\)
\(x=\frac{1.3}{2.2}+\frac{2.4}{3.3}+\frac{3.5}{4.4}+...+\frac{99.101}{100.100}\)
\(x=\frac{1.2...99}{2.3...100}.\frac{3.4...101}{2.3...100}\)
\(x=\frac{1}{100}.\frac{101}{2}\)
\(x=\frac{101}{200}\)
\(X=\frac{1.3}{2.2}+\frac{2.4}{3.3}+\frac{3.5}{4.4}+...+\frac{99.101}{100.100}\)
\(X=\frac{1.2.3....99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4....100}\)
\(X=\frac{1}{100}.\frac{101}{2}\)
\(X=\frac{101}{200}\)
Study well
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{81}=9\)
\(\sqrt{0,64}=0,8\)
\(\sqrt{\frac{49}{100}}=\frac{7}{10}\)
\(\sqrt{8100}=90\)
\(\sqrt{100=}10\)
\(\sqrt{0,01}=0,1\)
\(\sqrt{\frac{4}{25}}=\frac{2}{5}\)
\(\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}\)
\(\sqrt{81}=9\);\(\sqrt{0,64}=0,8\);\(\sqrt{\frac{49}{100}}=\frac{7}{10}\);\(\sqrt{8100}=90\); \(\sqrt{100}=10\); \(\sqrt{0,01}=0,1\); \(\sqrt{\frac{4}{25}}=\frac{2}{5}\); \(\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}=\frac{3}{110}\)
\(\sqrt{10000}+9820-\frac{930}{293}\)
\(=100+9820-\frac{930}{293}\)
\(=9920-\frac{930}{293}\)
\(=\frac{2905630}{293}\)
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