Các câu hỏi tương tự
Tính:
a, \(\frac{2}{5+2\sqrt{6}}+\frac{20}{\sqrt{6}-1}+\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}-\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
b,\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{n}+\sqrt{n+1}}\)
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) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
Bài 1: P=\(\frac{x\sqrt{x}+26\sqrt{x}-19}{x+2\sqrt{x}-3}-\frac{2\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}-3}{\sqrt{x}+3}\)
a) Rút gọn P
b) Tìm GTNN của P
Rút gọn các biểu thức sau :a,frac{3}{sqrt{5}-sqrt{2}}+frac{4}{sqrt{6}+sqrt{2}}b left(sqrt{20}-sqrt{45}+sqrt{5}right).sqrt{5}c,left(5sqrt{frac{1}{5}}+frac{1}{2}sqrt{20}-frac{5}{4}sqrt{frac{4}{5}+sqrt{5}}right):2sqrt{5}d 2sqrt{3}left(2sqrt{6}-sqrt{3}+1right)e sqrt{2+sqrt{3}}timessqrt{2-sqrt{3}}g frac{5sqrt{7}-7sqrt{5}+2sqrt{70}}{sqrt{35}}h left(sqrt{frac{2}{3}}+sqrt{frac{3}{2}}right)timessqrt{6}i left(1+sqrt{2}+sqrt{3}right)timesleft(1+sqrt{2}-sqrt{3}right)k frac{1}{sqrt{5}+sqrt{3}}-frac{1}{sqr...
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Rút gọn các biểu thức sau :
a,\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
b \(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right).\sqrt{5}\)
c,\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
d \(2\sqrt{3}\left(2\sqrt{6}-\sqrt{3}+1\right)\)
e \(\sqrt{2+\sqrt{3}}\times\sqrt{2-\sqrt{3}}\)
g \(\frac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)
h \(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}\right)\times\sqrt{6}\)
i \(\left(1+\sqrt{2}+\sqrt{3}\right)\times\left(1+\sqrt{2}-\sqrt{3}\right)\)
k \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
l \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
m \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
Giúp mình làm bài này vớiBài 1: TínhAsqrt{frac{5+2sqrt{6}}{5-2sqrt{6}}}+sqrt{frac{5-2sqrt{6}}{5+2sqrt{6}}}Bfrac{sqrt{2+sqrt{3}}}{2}divleft(frac{sqrt{2+sqrt{3}}}{2}-frac{2}{sqrt{6}}+frac{sqrt{2+sqrt{3}}}{2sqrt{3}}right)Cfrac{1}{sqrt{2}+2}+frac{1}{2sqrt{3}+3sqrt{2}}+...+frac{1}{99sqrt{100}+100sqrt{99}}Bài 2: Giải phương trình:a. sqrt{4x-20}+sqrt{x-5}-frac{1}{3}sqrt{9x-45}4b.frac{2sqrt{x}-7}{3}sqrt{x}-1c.5sqrt{x-1}-sqrt{36x-36}-sqrt{9x-9}sqrt{8x+12}Bài 3: Rút gọnMleft(frac{sqrt{a}}{2}-frac{1}{2sqrt...
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Giúp mình làm bài này với
Bài 1: Tính
A=\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
B=\(\frac{\sqrt{2+\sqrt{3}}}{2}\div\left(\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}\right)\)
C=\(\frac{1}{\sqrt{2}+2}+\frac{1}{2\sqrt{3}+3\sqrt{2}}+...+\frac{1}{99\sqrt{100}+100\sqrt{99}}\)
Bài 2: Giải phương trình:
a. \(\sqrt{4x-20}+\sqrt{x-5}-\frac{1}{3}\sqrt{9x-45}=4\)
b.\(\frac{2\sqrt{x}-7}{3}=\sqrt{x}-1\)
c.\(5\sqrt{x-1}-\sqrt{36x-36}-\sqrt{9x-9}=\sqrt{8x+12}\)
Bài 3: Rút gọn
\(M=\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\times\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a-1}}\right)\)
a. Tìm a để M>0
b. Tìm a để M<0
Q = \(\frac{x\sqrt{x}+26\sqrt{x}-19}{x+2\sqrt{x}-3}-\frac{2\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}-3}{\sqrt{x}+3}\)
Rút gọn Q , min Q ?
\(A=\frac{x\sqrt{x}+26\sqrt{x}-19}{x+2\sqrt{x}-3}-\frac{2\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}-3}{\sqrt{x}+3}\)
a,Rút gọn A
b,Tìm GTNN của A
Toán số 9, liên quan đến dạng căn. Các bạn giúp mình nhé, xin cảm ơn rất nhiều. :)1) left(sqrt{3-2sqrt{sqrt{3}-1}}+frac{sqrt{3}-1}{sqrt{2}}right)sqrt{sqrt{3}-1}2) left(sqrt{5+2sqrt{9sqrt{5}-19}}-sqrt{7-sqrt{5}}right):2sqrt{sqrt{5}-2}3) frac{sqrt{10+6sqrt{2}}-sqrt{10-6sqrt{2}}}{sqrt{5-sqrt{7}}}-sqrt{9+2sqrt{20}}4) frac{sqrt{5+sqrt{3}}+sqrt{5-sqrt{3}}}{sqrt{5+sqrt{22}}}-frac{sqrt{6-sqrt{24}}}{sqrt{3+sqrt{3}}-sqrt{3-sqrt{3}}}5) sqrt{5+2sqrt{14sqrt{5}-26}}-sqrt{4sqrt{5}-1+sqrt{80-8sqrt{5}}}6) frac{s...
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Toán số 9, liên quan đến dạng căn. Các bạn giúp mình nhé, xin cảm ơn rất nhiều. :)
1) \(\left(\sqrt{3-2\sqrt{\sqrt{3}-1}}+\frac{\sqrt{3}-1}{\sqrt{2}}\right)\sqrt{\sqrt{3}-1}\)
2) \(\left(\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}\right):2\sqrt{\sqrt{5}-2}\)
3) \(\frac{\sqrt{10+6\sqrt{2}}-\sqrt{10-6\sqrt{2}}}{\sqrt{5-\sqrt{7}}}-\sqrt{9+2\sqrt{20}}\)
4) \(\frac{\sqrt{5+\sqrt{3}}+\sqrt{5-\sqrt{3}}}{\sqrt{5+\sqrt{22}}}-\frac{\sqrt{6-\sqrt{24}}}{\sqrt{3+\sqrt{3}}-\sqrt{3-\sqrt{3}}}\)
5) \(\sqrt{5+2\sqrt{14\sqrt{5}-26}}-\sqrt{4\sqrt{5}-1+\sqrt{80-8\sqrt{5}}}\)
6) \(\frac{\sqrt{11+\sqrt{5}}+\sqrt{11-\sqrt{5}}}{\sqrt{11+2\sqrt{29}}}-\sqrt{3-2\sqrt{2}}\)
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)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)