TÍNH:
\(\frac{2+\sqrt{3}}{2-\sqrt{3}}+\frac{2-\sqrt{3}}{2+\sqrt{3}}-5\)
LU
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Thực hiện phép tính:
a)\(\frac{1}{3+\sqrt{2}}+\frac{1}{3-\sqrt{2}}\)
b) \(\frac{2}{3\sqrt{2}-3\sqrt{3}}-\frac{3}{2\sqrt{3}+3\sqrt{3}}\)
c)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
d)\(\frac{3}{2\sqrt{2}-3\sqrt{3}}-\frac{3}{2\sqrt{2}+3\sqrt{3}}\)
a) \(\frac{1}{3+\sqrt{2}}+\frac{1}{3-\sqrt{2}}=\frac{\left(3-\sqrt{2}\right)+\left(3+\sqrt{2}\right)}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}=\frac{6}{3^2-\left(\sqrt{2}\right)^2}=\frac{6}{7}\)
b) \(\frac{2}{3\sqrt{2}-3\sqrt{3}}-\frac{3}{2\sqrt{3}+3\sqrt{3}}=\frac{2\left(2\sqrt{3}+3\sqrt{3}\right)-3\left(3\sqrt{2}-3\sqrt{3}\right)}{\left(3\sqrt{2}-3\sqrt{3}\right)\left(2\sqrt{3}+3\sqrt{3}\right)}=\frac{19\sqrt{3}-9\sqrt{2}}{-45+15\sqrt{6}}=-\frac{13\sqrt{3}+10\sqrt{2}}{15}\)c) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\left(\sqrt{5}-\sqrt{3}\right)^2+\left(\sqrt{5}+\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\frac{5-2\sqrt{15}+3+5+2\sqrt{15}+3}{2}=\frac{16}{2}=8\)d) \(\frac{3}{2\sqrt{2}-3\sqrt{3}}-\frac{3}{2\sqrt{2}+3\sqrt{3}}=\frac{3\left(2\sqrt{2}+3\sqrt{3}\right)-3\left(2\sqrt{2}-3\sqrt{3}\right)}{\left(2\sqrt{2}-3\sqrt{3}\right)\left(2\sqrt{2}+3\sqrt{3}\right)}=-\frac{18\sqrt{3}}{19}\)
Giúp mình với, ko cần làm hết đâu. Tính!a)frac{2+sqrt{3}}{sqrt{2}+sqrt{2+sqrt{3}}}+frac{2-sqrt{3}}{sqrt{2}-sqrt{2-sqrt{3}}}b)frac{sqrt{2}}{2sqrt{2}+sqrt{3+sqrt{5}}}+frac{sqrt{2}}{2sqrt{2}-sqrt{3-sqrt{5}}}c)frac{left(5+2sqrt{6}right)left(49-20sqrt{6}right)sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}d)frac{frac{sqrt{2+sqrt{3}}}{2}}{frac{sqrt{2+sqrt{3}}}{2}-frac{2}{sqrt{6}}+frac{sqrt{2+sqrt{3}}}{2sqrt{3}}}
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Giúp mình với, ko cần làm hết đâu. Tính!
a)\(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
b)\(\frac{\sqrt{2}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{\sqrt{2}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
c)\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
d)\(\frac{\frac{\sqrt{2+\sqrt{3}}}{2}}{\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
\(\frac{A}{\sqrt{2}}=\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)
=\(\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}\) =\(\frac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}\) =\(\frac{6}{6}=1\)
\(\Rightarrow A=\sqrt{2}\)
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câu 1: tính
a)\(\frac{7}{\sqrt{10}-\sqrt{3}}-\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}-\frac{6}{\sqrt{3}}\)
b)\(\frac{\sqrt{27}-3\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{6}{3+\sqrt{3}}+\frac{3}{\sqrt{3}}\)
Tính \(\frac{2\sqrt{3}-4}{\sqrt{3}-1}+\frac{2\sqrt{2}-1}{\sqrt{2}-1}-\frac{1+\sqrt{6}}{\sqrt{2}+3}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+2\sqrt{12}}}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-2\sqrt{75}}}}\)
\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)
\(C=\sqrt{4+5}\)
\(C=3\)
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tính:a)frac{1}{1+sqrt{5}}+frac{1}{1-sqrt{5}}b)frac{sqrt{15}-sqrt{12}}{sqrt{5}-2}+frac{1}{2-sqrt{3}}c)frac{2}{sqrt{5}+1}+sqrt{frac{2}{3-sqrt{5}}}-5sqrt{frac{1}{5}}d)left(frac{5}{sqrt{15}-sqrt{10}}-frac{3sqrt{5}-5sqrt{3}}{sqrt{3}-sqrt{5}}right)^2e)frac{2}{sqrt{3}-sqrt{5}}+frac{3-2sqrt{3}}{sqrt{3}-2}
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tính:
a)\(\frac{1}{1+\sqrt{5}}+\frac{1}{1-\sqrt{5}}\)
b)\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}\)
c)\(\frac{2}{\sqrt{5}+1}+\sqrt{\frac{2}{3-\sqrt{5}}}-5\sqrt{\frac{1}{5}}\)
d)\(\left(\frac{5}{\sqrt{15}-\sqrt{10}}-\frac{3\sqrt{5}-5\sqrt{3}}{\sqrt{3}-\sqrt{5}}\right)^2\)
e)\(\frac{2}{\sqrt{3}-\sqrt{5}}+\frac{3-2\sqrt{3}}{\sqrt{3}-2}\)
Tính
\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
\(\frac{\frac{\sqrt{2+\sqrt{3}}}{2}}{\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
Tính: a)frac{3sqrt{2}-sqrt{6}}{3-sqrt{3}}+sqrt{frac{2-sqrt{2}}{2+sqrt{2}}}b) 6sqrt{frac{1}{3}}-frac{sqrt{3}-3}{sqrt{3}}+frac{3sqrt{2}-2sqrt{3}}{sqrt{2}-sqrt{3}}c) frac{3+sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-2sqrt{2}d) left(frac{sqrt{14}-sqrt{7}}{sqrt{2}-1}+frac{sqrt{15}-sqrt{5}}{sqrt{3}-1}right):frac{1}{sqrt{7}-sqrt{5}}Xin giúp 4 bài trên. Cảm ơn trước ạ!
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Tính: a)\(\frac{3\sqrt{2}-\sqrt{6}}{3-\sqrt{3}}+\sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}\)
b) \(6\sqrt{\frac{1}{3}}-\frac{\sqrt{3}-3}{\sqrt{3}}+\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{2}-\sqrt{3}}\)
c) \(\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-2\sqrt{2}\)
d) \(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
Xin giúp 4 bài trên. Cảm ơn trước ạ!
a,
\(\frac{\sqrt{6}\left(\sqrt{3}-1\right)}{\sqrt{3}\left(\sqrt{3}-1\right)}+\sqrt{\frac{\left(2-\sqrt{2}\right)^2}{\left(2+\sqrt{2}\right).\left(2-\sqrt{2}\right)}}\)
=\(\sqrt{2}+\frac{2-\sqrt{2}}{\sqrt{2}}\)
=\(\sqrt{2}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}}\)
=\(\sqrt{2}+\sqrt{2}-1\)
=\(2\sqrt{2}-1\)
còn tiếp
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b=,\(\frac{6\sqrt{3}}{3}-\frac{\sqrt{3}\left(1-\sqrt{3}\right)}{\sqrt{3}}-\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\sqrt{2}-\sqrt{3}}\)
=\(6-1+\sqrt{3}-\sqrt{6}\)
=\(5+\sqrt{3}+\sqrt{6}\)
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Tính:
a/ \(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
b/ \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\$\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
Tínhfrac{2sqrt{3}}{sqrt{2}+sqrt{2}+sqrt{3}}+frac{2-sqrt{3}}{sqrt{2}-sqrt{2}-sqrt{3}}frac{sqrt{2}}{2sqrt{2}+sqrt{3}+sqrt{5}}+frac{sqrt{2}}{2sqrt{2}-sqrt{3}-sqrt{5}}frac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+4}{sqrt{2}+sqrt{3}+sqrt{4}}frac{left(5+2sqrt{6}right)left(49-20sqrt{6}right)sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}frac{frac{sqrt{2+sqrt{3}}}{2}}{frac{sqrt{2+sqrt{3}}}{2}-frac{2}{sqrt{6}}+frac{sqrt{2+sqrt{3}}}{2sqrt{3}}}Mọi người giúp em với!!!!! một trong 5 câu đó cũng đc!!!! Ai tốt thì giúp em hết l...
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Tính
\(\frac{2\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
\(\frac{\sqrt{2}}{2\sqrt{2}+\sqrt{3}+\sqrt{5}}+\frac{\sqrt{2}}{2\sqrt{2}-\sqrt{3}-\sqrt{5}}\)
\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
\(\frac{\frac{\sqrt{2+\sqrt{3}}}{2}}{\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
Mọi người giúp em với!!!!! một trong 5 câu đó cũng đc!!!! Ai tốt thì giúp em hết luôn nha!!!!! Em cảm ơn !!!!!
Bài 1: Thực hiện phép tính1) A frac{4}{3+sqrt{5}}-frac{8}{1+sqrt{5}}+frac{15}{sqrt{5}}2) A sqrt{frac{3sqrt{3}-4}{2sqrt{3}+1}}+sqrt{frac{sqrt{3}+4}{5-2sqrt{3}}}3) sqrt{14-8sqrt{3}}-sqrt{24-12sqrt{3}}4) B 5(sqrt{2+sqrt{3}}+sqrt{3-sqrt{5}}-sqrt{frac{5}{2}})2 + ( sqrt{2-sqrt{3}}+sqrt{3+sqrt{5}}-sqrt{frac{3}{2}})25) frac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+frac{1}{sqrt{2}-sqrt{2-sqrt{3}}}
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Bài 1: Thực hiện phép tính
1) A= \(\frac{4}{3+\sqrt{5}}-\frac{8}{1+\sqrt{5}}+\frac{15}{\sqrt{5}}\)
2) A= \(\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
3) \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
4) B= 5(\(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\frac{5}{2}}\))2 + ( \(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\frac{3}{2}}\))2
5) \(\frac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)