a) \(10\sqrt{0,01}.\sqrt{\frac{16}{9}}+3\sqrt{49}-\frac{1}{6}\sqrt{4}\)

\(=10\sqrt{\frac{10}{100}}.\sqrt{\frac{4^2}{3^2}}+3.\sqrt{7^2}-\frac{1}{6}\sqrt{2^2}\)

\(=10.\frac{\sqrt{10}}{10}.\frac{4}{3}+3.7-\frac{1}{6}.2\)

\(=\frac{4\sqrt{10}}{3}+27-\frac{1}{3}\)

\(=\frac{4}{3}\sqrt{10}+\frac{80}{3}\)

b) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(0,8-\frac{3}{4}\right)^2\)

\(=\frac{17}{12}.\left(\frac{4}{5}-\frac{3}{4}\right)^2\)

\(=\frac{17}{12}.\left(\frac{1}{20}\right)^2\)

\(=\frac{17}{12}.\frac{1}{400}\)

\(=\frac{17}{4800}\)

a.\(\frac{133}{6}\)

b.\(\frac{17}{4800}\)

a) \(\left(\frac{2^2}{5}\right)+5\frac{1}{2}.\left(4,5-2,5\right)+\frac{2^3}{-4}\)

\(=\frac{4}{5}+\frac{11}{2}.2+\frac{-8}{4}\)

\(=\frac{4}{5}+11-2\)

\(=\frac{4}{5}+9\)

\(=\frac{49}{9}\)

b) \(\left(-2^3\right)+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)

\(=-8+4-5+64\)

= 55

c) \(\frac{\sqrt{3^2+\sqrt{39}^2}}{\sqrt{91^2}-\sqrt{\left(-7\right)^2}}\)

\(=\frac{\sqrt{9+39}}{91-\sqrt{49}}\)

\(=\frac{\sqrt{48}}{91-7}\)

\(=\frac{4\sqrt{3}}{84}\)

\(=\frac{\sqrt{3}}{41}\)

d) Xem lại đề nhé em!

e) \(\sqrt{25}-3\sqrt{\frac{4}{9}}\)

\(=5-3.\frac{2}{3}\)

= 5 - 2

= 3

h) \(\left(-3^2\right).\frac{1}{3}-\sqrt{49}+\left(5^3\right):\sqrt{25}\)

\(=-9.\frac{1}{3}-7+125:5\)

\(=-3-7+25\)

= 15

Ta có: \(\sqrt[k+1]{\frac{k+1}{k}}>1\) với \(k=1,2,...,n\)

Áp dụng BĐT AM-GM cho \(k+1\) số ta có: 

\(\sqrt[k+1]{\frac{k+1}{k}}=\sqrt[k+1]{\frac{1.1...1}{k}\cdot\frac{k+1}{k}}\)

\(< \frac{1+1+1+...+1+\frac{k+1}{k}}{k+1}=\frac{k}{k+1}+\frac{1}{k}=1+\frac{1}{k\left(k+1\right)}\)

Suy ra \(1< \sqrt[k+1]{\frac{k+1}{k}}< 1+\left(\frac{1}{k}-\frac{1}{k+1}\right)\)

Lần lượt cho \(k=1,2,3,...,n\) rồi cộng lại ta được:

\(n< \sqrt{2}+\sqrt[3]{\frac{3}{2}}+...+\sqrt[n+1]{\frac{n+1}{n}}< n+1-\frac{1}{n}< n+1\)

Vậy \(\left[a\right]=n\)

x+1/3-4=-1

=>x+1/3=-1+4

=>x+1/3=3

=>x =3-1/3

=>x =8/3

Vậy x = 8/3

(2/25-1,008):4/7:(13/4-6/5/9)*36/17

=(2/25-126/125).7/4:(13/4-59/9)*36/17

=(10/125-126/125).7/4:(117/36-236/36)*36/17

=-116/125.7/4.(-36/119).36/17

=-203/125.(-1296/2023)=263088/252875

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