a) 9
b)90
c)8
d)7/10
e)2/5

a=9

b=90

c=2

d=0,7

e=0,2

\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{899}+\sqrt{900}}\)

=\(\frac{\sqrt{1}-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+....+\frac{\sqrt{899}-\sqrt{900}}{899-900}\)

\(=\frac{\sqrt{1}-\sqrt{2}}{-1}+\frac{\sqrt{2}-\sqrt{3}}{-1}+....+\frac{\sqrt{899}-\sqrt{900}}{-1}\)

\(=\frac{\sqrt{1}-\sqrt{2}+\sqrt{2}-\sqrt{3}+....+\sqrt{899}-\sqrt{900}}{-1}\)

\(=\frac{\sqrt{1}-\sqrt{900}}{-1}\)

\(=\frac{1-30}{-1}=\frac{-29}{-1}=29\)

=

\(\sqrt{14+\sqrt{16900}}-\sqrt{19+\sqrt{900}}+\sqrt{45+\sqrt{3025}}\)

\(=\sqrt{14+\sqrt{130^2}}-\sqrt{19+\sqrt{30^2}}+\sqrt{45+\sqrt{55^2}}\)

\(=\sqrt{14+130}-\sqrt{19+30}+\sqrt{45+55}\)

\(=\sqrt{144}-\sqrt{49}+\sqrt{100}\)

\(=\sqrt{12^2}-\sqrt{7^2}+\sqrt{10^2}\)

\(=12-7+10\)

\(=5+10\)

\(=15\)

Mk nghĩ bạn cx lm đc mak cần J đăng :)

\(\sqrt{14+\sqrt{16900}}-\sqrt{19+\sqrt{900}}+\sqrt{45+\sqrt{3025}}\)

\(=\sqrt{14+130}-\sqrt{19+30}+\sqrt{45+55}=12-7+10=15\)

Mk đang rảnh nên thik lm mấy câu dễ dễ "___"

Xét \(a_n=\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{\left(n+1\right)\sqrt{n}-n\sqrt{n+1}}{\left(n+1\right)^2n-n^2\left(n+1\right)}\)

\(=\frac{\left(n+1\right)\sqrt{n}-n\sqrt{n+1}}{n\left(n+1\right)}=\frac{\sqrt{n}}{n}-\frac{\sqrt{n+1}}{n+1}\)

\(\Rightarrow S=\frac{\sqrt{1}}{1}-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}+...+\frac{\sqrt{899}}{899}-\frac{\sqrt{900}}{900}\)

\(S=1-\frac{\sqrt{900}}{900}=1-\frac{1}{30}=\frac{29}{30}\)

\(=\dfrac{\left(\sqrt{1}-\sqrt{2}\right)}{1-2}+\dfrac{\sqrt{2}-\sqrt{3}}{2-3}+....+\dfrac{\sqrt{899}-\sqrt{900}}{899-900}\\ =\sqrt{900}-\sqrt{899}+\sqrt{899}-.....+\sqrt{3}-\sqrt{2}+\sqrt{2}-\sqrt{1}=\\ =\sqrt{900}-\sqrt{1}\\ =30-1=29\)

\(a,\sqrt{81}=9\)

\(b.\sqrt{8100}=90\)

\(c,\sqrt{64}=8\)

\(d,\sqrt{25}=5\)

\(e,\sqrt{0,64}=0,8\)

\(f,\sqrt{10000}=100\)

\(g,\sqrt{0,01}=0,1\)

\(h,\sqrt{\frac{49}{100}}=\frac{7}{10}\)

\(i,\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}\)

\(j,\sqrt{\frac{4}{25}}=\frac{2}{5}\)

~Study well~

#JDW

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.

\(\sqrt{81}=9\)

\(\sqrt{0,64}=0,8\)

\(\sqrt{\frac{49}{100}}=\frac{7}{10}\)

\(\sqrt{8100}=90\)

\(\sqrt{100=}10\)

\(\sqrt{0,01}=0,1\)

\(\sqrt{\frac{4}{25}}=\frac{2}{5}\)

\(\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}\)

\(\sqrt{81}=9\);\(\sqrt{0,64}=0,8\);\(\sqrt{\frac{49}{100}}=\frac{7}{10}\);\(\sqrt{8100}=90\); \(\sqrt{100}=10\); \(\sqrt{0,01}=0,1\); \(\sqrt{\frac{4}{25}}=\frac{2}{5}\); \(\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}=\frac{3}{110}\)

\(\sqrt{81}=9\)

\(\sqrt{0.64}=\sqrt{\frac{64}{100}}=\frac{8}{10}\);\(\sqrt{\frac{49}{100}}=\frac{7}{10}\)

\(\sqrt{8100}=\sqrt{81}.\sqrt{100}=9.10=90\);\(\sqrt{100}=10\)

\(\sqrt{0,01}=0,1\);\(\sqrt{\frac{4}{25}}=\frac{2}{5}\);\(\sqrt{\frac{0,09}{121}}=\frac{0,3}{11}\)

\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{899}+\sqrt{900}}\)

\(=\frac{\sqrt{2}-\sqrt{1}}{\left(\sqrt{2}-\sqrt{1}\right)\left(\sqrt{2}+\sqrt{1}\right)}+\frac{\sqrt{3}-\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}+...+\frac{\sqrt{900}-\sqrt{899}}{\left(\sqrt{900}-\sqrt{899}\right)\left(\sqrt{900}+\sqrt{899}\right)}\)

\(=\frac{\sqrt{2}-1}{2-1}+\frac{\sqrt{3}-\sqrt{2}}{3-2}+...+\frac{\sqrt{900}-\sqrt{899}}{900-899}\)

\(=\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{3}+...+\sqrt{900}-\sqrt{899}\)

\(=\sqrt{900}-\sqrt{1}\)

\(=30-1\)

\(=29\)