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Rút gọn biểu thức 1) frac{sqrt{5+2sqrt{6}}+sqrt{8+2sqrt{15}}}{sqrt{7+2sqrt{10}}}2) left(2+frac{3+sqrt{3}}{sqrt{3}+1}right)left(2+frac{3-sqrt{3}}{sqrt{3}-1}right):left(sqrt{5}-2right)3) left(frac{15}{sqrt{6}+1}+frac{4}{sqrt{6}-2}-frac{12}{3-sqrt{6}}right).left(sqrt{6}+11right)4) frac{1}{1+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+...+frac{1}{sqrt{99}+sqrt{100}}5) frac{1}{1-sqrt{2}}-frac{1}{sqrt{2}-sqrt{3}}+frac{1}{sqrt{3}-sqrt{4}}-...-frac{1}{sqrt{98}-sqrt{99}}+frac{1}{sqrt{99}-s...
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Rút gọn biểu thức
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)
1) Rút gọn biểu thức:
a) \(\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\)
b) \(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}-\sqrt{6}\)
c) \(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
d) \(\frac{4}{\sqrt{5}-\sqrt{2}}+\frac{3}{\sqrt{5}-2}-\frac{2}{\sqrt{3}-2}+\frac{\sqrt{3}-1}{6}\)
1. Tính:
a) \(\frac{\sqrt{7}-5}{2}-\frac{6-2\sqrt{7}}{4}+\frac{6}{\sqrt{7}-2}-\frac{5}{4+\sqrt{7}}\)
b) \(\frac{2}{\sqrt{6}-2}+\frac{2}{\sqrt{6}+2}+\frac{5}{\sqrt{6}}\)
c) \(\frac{1}{\sqrt{3}}+\frac{1}{3\sqrt{2}}+\frac{1}{\sqrt{3}}\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}\)
d) \(\frac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
Thực hiện phép tínha) left(2-sqrt{3}right)^2-sqrt{4-2sqrt{3}}+sqrt{12}b)frac{2sqrt{12}-sqrt{6}}{2sqrt{6}-sqrt{3}}+frac{10+sqrt{5}}{2sqrt{15}+sqrt{3}}c)left(frac{3+2sqrt{3}}{sqrt{3}+2}+frac{2+sqrt{2}}{sqrt{2}+1}right):left(sqrt{2}+sqrt{3}right)d)sqrt{10-4sqrt{6}}+sqrt{33-12sqrt{6}}e)sqrt{16-6sqrt{7}}+sqrt{32-8sqrt{7}}f)sqrt{28-16sqrt{3}}+sqrt{73-40sqrt{3}}
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Thực hiện phép tính
a) \(\left(2-\sqrt{3}\right)^2-\sqrt{4-2\sqrt{3}}+\sqrt{12}\)
b)\(\frac{2\sqrt{12}-\sqrt{6}}{2\sqrt{6}-\sqrt{3}}+\frac{10+\sqrt{5}}{2\sqrt{15}+\sqrt{3}}\)
c)\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right):\left(\sqrt{2}+\sqrt{3}\right)\)
d)\(\sqrt{10-4\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e)\(\sqrt{16-6\sqrt{7}}+\sqrt{32-8\sqrt{7}}\)
f)\(\sqrt{28-16\sqrt{3}}+\sqrt{73-40\sqrt{3}}\)
1/ frac{2}{3-sqrt{7}}sqrt{frac{6sqrt{2}-2sqrt{14}}{3sqrt{2}+sqrt{14}}}2/ sqrt{6+2sqrt{sqrt{5}-sqrt{13-sqrt{48}}}}3/ frac{sqrt{3-2sqrt{2}}}{sqrt{17-12sqrt{2}}}-frac{sqrt{3+2sqrt{2}}}{sqrt{17+12sqrt{2}}}4/ frac{24}{sqrt{7}+1}+frac{4}{3+sqrt{7}}-frac{3}{sqrt{7}+2}left(4-sqrt{7}right)5/ sqrt{7-3sqrt{5}}left(7+3sqrt{5}right)left(3sqrt{2}+sqrt{10}right)
Đọc tiếp
1/ \(\frac{2}{3-\sqrt{7}}\sqrt{\frac{6\sqrt{2}-2\sqrt{14}}{3\sqrt{2}+\sqrt{14}}}\)
2/ \(\sqrt{6+2\sqrt{\sqrt{5}-\sqrt{13-\sqrt{48}}}}\)
3/ \(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
4/ \(\frac{24}{\sqrt{7}+1}+\frac{4}{3+\sqrt{7}}-\frac{3}{\sqrt{7}+2}\left(4-\sqrt{7}\right)\)
5/ \(\sqrt{7-3\sqrt{5}}\left(7+3\sqrt{5}\right)\left(3\sqrt{2}+\sqrt{10}\right)\)
Rút gọn biểu thức 1)frac{15}{3sqrt{20}}2) frac{sqrt{15}-sqrt{6}}{sqrt{2}-sqrt{5}}3) frac{3}{sqrt{5}-sqrt{2}}+frac{4}{sqrt{6}+sqrt{2}}4) sqrt{frac{3}{20}}+sqrt{frac{1}{60}}-2sqrt{frac{1}{15}}5) left(sqrt{20}-sqrt{45}+sqrt{5}right)sqrt{5}6)left(2+sqrt{5}right)^2-left(2+sqrt{5}right)^27) left(5sqrt{frac{1}{5}}+frac{1}{2}sqrt{20}-frac{5}{4}sqrt{frac{4}{5}+sqrt{5}}right):2sqrt{5}8)frac{1}{3}sqrt{48}+3sqrt{75}-sqrt{27}-10sqrt{1frac{1}{3}}9) 2sqrt{3}left(2sqrt{6}-sqrt{3}+1right)10) left(5sqrt{3}+3sqrt{...
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Rút gọn biểu thức
1)\(\frac{15}{3\sqrt{20}}\)
2) \(\frac{\sqrt{15}-\sqrt{6}}{\sqrt{2}-\sqrt{5}}\)
3) \(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
4) \(\sqrt{\frac{3}{20}}+\sqrt{\frac{1}{60}}-2\sqrt{\frac{1}{15}}\)
5) \(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
6)\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
7) \(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
8)\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\frac{1}{3}}\)
9) \(2\sqrt{3}\left(2\sqrt{6}-\sqrt{3}+1\right)\)
10) \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
11) \(\sqrt{\sqrt{10}+1}.\sqrt{\sqrt{10}-1}\)
12) \(\frac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)
13) \(\sqrt{\frac{3}{4}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{12}}\)
14) \(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}\right)\sqrt{6}\)
15 ) \(\sqrt{\frac{4}{3}}+\sqrt{12}-\frac{4}{3}\sqrt{\frac{3}{4}}\)
16) \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
17) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
Rút gọn
a)\(\frac{2\sqrt{5\:\:\:}-4\sqrt{10}}{3\sqrt{10}}\)
b)\(\frac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)
c)\(\frac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)
d)\(\left(\sqrt{3}-1\right)\sqrt{2\sqrt{19+8\sqrt{3}}-4}\)
a) frac{2sqrt{5}-4sqrt{10}}{3sqrt{10}}b)frac{6sqrt{6}-2sqrt{12}+3-sqrt{2}}{2sqrt{6}+1}c)frac{sqrt{3left(3-sqrt{11}right)^2}}{sqrt{6}left(3-sqrt{11}right)}d)frac{5sqrt{7}-4sqrt{35}+7sqrt{5}}{sqrt{35}}e) left(sqrt{3}-1right)sqrt{2sqrt{19+8sqrt{3}-4}}g) sqrt{47+sqrt{5}}.sqrt{7-sqrt{2+sqrt{5}}.}sqrt{7+sqrt{2+sqrt{5}}}
Đọc tiếp
a) \(\frac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}\)
b)\(\frac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)
c)\(\frac{\sqrt{3\left(3-\sqrt{11}\right)^2}}{\sqrt{6}\left(3-\sqrt{11}\right)}\)
d)\(\frac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)
e) \(\left(\sqrt{3}-1\right)\sqrt{2\sqrt{19+8\sqrt{3}-4}}\)
g) \(\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}.}\sqrt{7+\sqrt{2+\sqrt{5}}}\)
sqrt{5-sqrt{6}+sqrt{10}-sqrt{15}}-frac{sqrt{16-4sqrt{15}}}{2}frac{sqrt{1+2sqrt{27sqrt{2}-38}}-sqrt{5-3sqrt{2}}}{sqrt{3sqrt{2}}-4}sqrt{3+sqrt{2}+sqrt{3}+sqrt{6}}-sqrt{2+sqrt{3}}frac{3-sqrt{6+sqrt{3+sqrt{6+sqrt{3}}}}}{3-sqrt{3+sqrt{6+sqrt{3}}}}+frac{2+sqrt{6+sqrt{3+sqrt{6+sqrt{3}}}}}{3+sqrt{6+sqrt{3+sqrt{6+sqrt{3}}}}}sqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}}Giải dùm mình nhé!!!!!!! Không cần giải hết đâu!!!!! Mọi người thấy bài nào dạng giống nhau thì giải 1 lần rồi nói mình đó là bài nà...
Đọc tiếp
\(\sqrt{5-\sqrt{6}+\sqrt{10}-\sqrt{15}}-\frac{\sqrt{16-4\sqrt{15}}}{2}\)
\(\frac{\sqrt{1+2\sqrt{27\sqrt{2}-38}}-\sqrt{5-3\sqrt{2}}}{\sqrt{3\sqrt{2}}-4}\)
\(\sqrt{3+\sqrt{2}+\sqrt{3}+\sqrt{6}}-\sqrt{2+\sqrt{3}}\)
\(\frac{3-\sqrt{6+\sqrt{3+\sqrt{6+\sqrt{3}}}}}{3-\sqrt{3+\sqrt{6+\sqrt{3}}}}+\frac{2+\sqrt{6+\sqrt{3+\sqrt{6+\sqrt{3}}}}}{3+\sqrt{6+\sqrt{3+\sqrt{6+\sqrt{3}}}}}\)
\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
Giải dùm mình nhé!!!!!!! Không cần giải hết đâu!!!!! Mọi người thấy bài nào dạng giống nhau thì giải 1 lần rồi nói mình đó là bài nào lun nha!!!!!!!!!! Mình cần rất gấp ạ!!!!!! Mong các bạn giúp mình