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Chương I - Căn bậc hai. Căn bậc ba
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Tính giá trị các biểu thức sau
1.dfrac{1}{sqrt{1}-sqrt{2}}-dfrac{1}{sqrt{2}-sqrt{3}}+dfrac{1}{sqrt{3}-sqrt{4}}-dfrac{1}{sqrt{4}-sqrt{5}}+dfrac{1}{sqrt{5}-sqrt{6}}-dfrac{1}{sqrt{6}-sqrt{7}}+dfrac{1}{sqrt{7}-sqrt{8}}-dfrac{1}{sqrt{8}-sqrt{9}}
2.dfrac{1}{2sqrt{1}+1sqrt{2}}+dfrac{1}{3sqrt{2}+2sqrt{3}}+dfrac{1}{4sqrt{3}+3sqrt{4}}+dfrac{1}{5sqrt{4}+4sqrt{5}}+dfrac{1}{6sqrt{5}+5sqrt{6}}+dfrac{1}{7sqrt{6}+6sqrt{7}}
giúp mk vs ạ
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Tính giá trị các biểu thức sau
1.\(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-\dfrac{1}{\sqrt{4}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{9}}\)
2.\(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+\dfrac{1}{5\sqrt{4}+4\sqrt{5}}+\dfrac{1}{6\sqrt{5}+5\sqrt{6}}+\dfrac{1}{7\sqrt{6}+6\sqrt{7}}\)
giúp mk vs ạ
Chứng minh rằng:
\(\dfrac{87}{89}< \dfrac{1}{2\sqrt{1}}+\dfrac{1}{3\sqrt{2}}+...+\dfrac{1}{2011\sqrt{2010}}< \dfrac{88}{45}\)
rút gọn :
a)left(dfrac{sqrt{15}-sqrt{5}}{1-sqrt{3}}+dfrac{sqrt{14}-sqrt{7}}{1-sqrt{2}}right):dfrac{1}{sqrt{7}-sqrt{5}}
b) sqrt{dfrac{3sqrt{3}-4}{2sqrt{3}+1}}+sqrt{dfrac{sqrt{3}+4}{5-2sqrt{3}}}
c) dfrac{2sqrt{5}-5sqrt{2}}{sqrt{2}-sqrt{5}}+dfrac{6}{2-sqrt{10}}+sqrt{67+12sqrt{7}}
d) left(dfrac{sqrt{5}}{sqrt{2}+1}+dfrac{14}{2sqrt{2}-1}-dfrac{6}{2-sqrt{2}}right).sqrt{17-12sqrt{2}}
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rút gọn :
a)\(\left(\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}+\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
b) \(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
c) \(\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\dfrac{6}{2-\sqrt{10}}+\sqrt{67+12\sqrt{7}}\)
d) \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right).\sqrt{17-12\sqrt{2}}\)
pdfrac{2}{1-sqrt{2}}-dfrac{2}{1+sqrt{2}}
Qleft(dfrac{sqrt{6}-sqrt{2}}{1-sqrt{3}}-dfrac{5}{sqrt{5}}right)cdotleft(sqrt{5}-sqrt{2}right)
Rdfrac{2}{7+4sqrt{3}}+dfrac{2}{7-4sqrt{3}}
Sdfrac{2}{sqrt{5}+1}-sqrt{dfrac{2}{3-sqrt{5}}}
Tdfrac{4}{1-sqrt{3}}-dfrac{sqrt{15}+sqrt{3}}{1+sqrt{5}}
Uleft(dfrac{1}{2-sqrt{5}}+dfrac{2}{sqrt{5}+sqrt{3}}right):dfrac{1}{sqrt{21-12sqrt{3}}}
Vdfrac{2}{sqrt{3}-1}-sqrt{dfrac{2}{6-3sqrt{3}}}
Wdfrac{5sqrt{3}}{sqrt{3-sqrt{5}}-sqrt{3}}-dfrac{5sqrt{3}}{sqrt{3-sqrt{5}}+sqr...
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\(p=\dfrac{2}{1-\sqrt{2}}-\dfrac{2}{1+\sqrt{2}}\)
\(Q=\left(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}\right)\cdot\left(\sqrt{5}-\sqrt{2}\right)\)
\(R=\dfrac{2}{7+4\sqrt{3}}+\dfrac{2}{7-4\sqrt{3}}\)
\(S=\dfrac{2}{\sqrt{5}+1}-\sqrt{\dfrac{2}{3-\sqrt{5}}}\)
\(T=\dfrac{4}{1-\sqrt{3}}-\dfrac{\sqrt{15}+\sqrt{3}}{1+\sqrt{5}}\)
\(U=\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\right):\dfrac{1}{\sqrt{21-12\sqrt{3}}}\)
\(V=\dfrac{2}{\sqrt{3}-1}-\sqrt{\dfrac{2}{6-3\sqrt{3}}}\)
\(W=\dfrac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}-\sqrt{3}}-\dfrac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}+\sqrt{3}}\)
\(Y=\dfrac{\sqrt{2}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}\)
rút gọn biểu thức
a.\(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b.\(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c.\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d.\(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
4 tháng 7 2021 lúc 16:06
* Chứng minh đẳng thức
\(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=2\sqrt{x-1}\) với x ≥ 2
* Trục căn thức ở mẫu
a.\(\dfrac{1}{\sqrt{5}+\sqrt{7}}\)
b.\(\dfrac{2}{5-\sqrt{2}-\sqrt{3}}\)
c.\(\dfrac{7}{\sqrt{5}-\sqrt{3}+\sqrt{5}}\)
5 tháng 7 2021 lúc 16:10
* Rút gọn biểu thức
a. \(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b. \(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c. \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d. \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
6 tháng 7 2021 lúc 20:28
- Rút gọn biểu thức
a. \(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b. \(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c. \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d. \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
Rút gọn:
A dfrac{4+sqrt{7}}{3sqrt{2}+sqrt{4+sqrt{7}}}+dfrac{4-sqrt{7}}{3sqrt{2}-sqrt{4-sqrt{7}}}
B dfrac{3sqrt{2}+sqrt{11}}{sqrt{2}+sqrt{6+sqrt{11}}}+dfrac{3sqrt{2}-sqrt{11}}{sqrt{2}-sqrt{6-sqrt{11}}}+18
C dfrac{1}{sqrt{3}+sqrt{5}}+dfrac{1}{sqrt{5}+sqrt{7}}+...+dfrac{1}{sqrt{2n+1}+sqrt{2n+3}}với n thuộc N*
D left(sqrt{3}+1right)left(sqrt{5}-1right)left(sqrt{15}-1right)left(7-2sqrt{3}+sqrt{5}right)
Edfrac{left(4+sqrt{3}right)}{sqrt[]{1}+sqrt{3}}+dfrac{left(8+sqrt{15}right)}{sqrt{3}+sqrt...
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Rút gọn:
A = \(\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
B = \(\dfrac{3\sqrt{2}+\sqrt{11}}{\sqrt{2}+\sqrt{6+\sqrt{11}}}+\dfrac{3\sqrt{2}-\sqrt{11}}{\sqrt{2}-\sqrt{6-\sqrt{11}}}+18\)
C = \(\dfrac{1}{\sqrt{3}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+...+\dfrac{1}{\sqrt{2n+1}+\sqrt{2n+3}}\)với n thuộc N*
D = \(\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)\left(\sqrt{15}-1\right)\left(7-2\sqrt{3}+\sqrt{5}\right)\)
E=\(\dfrac{\left(4+\sqrt{3}\right)}{\sqrt[]{1}+\sqrt{3}}+\dfrac{\left(8+\sqrt{15}\right)}{\sqrt{3}+\sqrt{5}}+...+\dfrac{2k+\sqrt{k^2-1}}{\sqrt{k-1}+\sqrt{k+1}}+...+\dfrac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)
F = \(\left(\dfrac{2a+1}{a\sqrt{a}-1}-\dfrac{\sqrt{a}}{a+\sqrt{a}+1}\right)\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\) với a >= 0 và a khác 1