Tính t=\(\sqrt[3]{8\left(7+5\sqrt{2}\right)}+\sqrt[3]{216\left(7-5\sqrt{2}\right)}+4\sqrt{2}-7\)
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Chứng minh đẳng thức
\(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}+1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=-1,5\)
\(\left(4-\sqrt{7}\right)^2=4^2-2\cdot4\cdot\sqrt{7}+7\)
\(=16-8\sqrt{7}+7=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
\(=\sqrt{5-2\cdot\sqrt{5}\cdot2+4}-\sqrt{5}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\)
\(=\left|\sqrt{5}-2\right|-\sqrt{5}\)
\(=\sqrt{5}-2-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}+1}\)
\(=\dfrac{\sqrt{3-2\cdot\sqrt{3}\cdot1+1}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\)
\(=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\)
\(=\dfrac{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}=\dfrac{3-1}{2-1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right)\cdot\dfrac{1}{\sqrt{6}}\)
\(=\left(\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-\dfrac{6\sqrt{6}}{3}\right)\cdot\dfrac{1}{\sqrt{6}}\)
\(=\left(\dfrac{1}{2}\sqrt{6}-2\sqrt{6}\right)\cdot\dfrac{1}{\sqrt{6}}\)
\(=\dfrac{1}{2}-2=-\dfrac{3}{2}=-1,5\)
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Chứng minh đẳng thức
\(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}-1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=-1,5\)
Tính:1) ( 2sqrt{5}-sqrt{7} ) left(2sqrt{5}+sqrt{7}right)2) left(5sqrt{2}+2sqrt{3}right)left(2sqrt{3}-5sqrt{2}right)3) sqrt{left(sqrt{7}-2right)^2}+sqrt{left(sqrt{7}+2right)^2}4) sqrt{left(sqrt{3}+sqrt{2}right)^2}+sqrt{left(sqrt{3}-sqrt{2}right)^2}5) left(sqrt{5}-sqrt{6}right)^26) left(sqrt{3}-sqrt{5}right)^27) left(2sqrt{2}+sqrt{3}right)^2
Đọc tiếp
Tính:
1) ( \(2\sqrt{5}-\sqrt{7}\) ) \(\left(2\sqrt{5}+\sqrt{7}\right)\)
2) \(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)
3) \(\sqrt{\left(\sqrt{7}-2\right)^2}+\sqrt{\left(\sqrt{7}+2\right)^2}\)
4) \(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
5) \(\left(\sqrt{5}-\sqrt{6}\right)^2\)
6) \(\left(\sqrt{3}-\sqrt{5}\right)^2\)
7) \(\left(2\sqrt{2}+\sqrt{3}\right)^2\)
\(1,=20-7=13\\ b,=12-50=-38\\ c,=\sqrt{7}-2+\sqrt{7}+2=2\sqrt{7}\\ d,=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\\ e,=11+2\sqrt{30}\\ f,=8-2\sqrt{15}\\ g,=11+2\sqrt{6}\)
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1) \(=\left(2\sqrt{5}\right)^2-\left(\sqrt{7}\right)^2=20-7=13\)
2) \(=\left(2\sqrt{3}\right)^2-\left(5\sqrt{2}\right)^2=12-50=-38\)
3) \(=\sqrt{7}-2+\sqrt{7}+2=2\sqrt[]{7}\)
4) \(=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\)
5) \(=5+6-2\sqrt{5.6}=11-2\sqrt{30}\)
6) \(=3+5-2\sqrt{3.5}=8-4\sqrt{2}\)
7) \(=\left(2\sqrt{2}\right)^2+\left(\sqrt{3}\right)^2+2\sqrt{2\sqrt{2}.3}=11+2\sqrt{6\sqrt{2}}\)
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Tính
a/left(frac{2sqrt{3}-sqrt{6}}{sqrt{8}-2}-frac{sqrt{216}}{3}right).frac{1}{sqrt{6}}
b/left(frac{5}{4-sqrt{11}}+frac{1}{3+sqrt{7}}-frac{6}{sqrt{7}-2}-frac{sqrt{7}-5}{2}right)
c/left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}
d/frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
Đọc tiếp
Tính
a/\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
b/\(\left(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\right)\)
c/\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
d/\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}=\left(\frac{\sqrt{7}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}+\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}=\left(\frac{-\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\frac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}=\left(-\sqrt{7}-\sqrt{5}\right):\frac{1}{\sqrt{7}-\sqrt{5}}=\frac{\sqrt{5}-\sqrt{7}}{\sqrt{7}+\sqrt{5}}=\frac{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}+\sqrt{7}\right)}{\left(\sqrt{7}+\sqrt{5}\right)^2}=\frac{2}{12+2\sqrt{35}}\)
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\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}=\frac{\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}+\frac{\left(\sqrt{5}+\sqrt{3}\right)^2}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+3\right)}-\frac{\sqrt{5}+1}{\sqrt{5}-1}=\frac{8-2\sqrt{15}}{2}+\frac{8+2\sqrt{15}}{2}-\frac{\left(\sqrt{5}+1\right)^2}{4}=8-\frac{6+2\sqrt{5}}{4}=\frac{26-2\sqrt{5}}{4}\)
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Tínha/left(frac{2sqrt{3}-sqrt{6}}{sqrt{8}-2}-frac{sqrt{216}}{3}right).frac{1}{sqrt{6}}b/left(frac{5}{4-sqrt{11}}+frac{1}{3+sqrt{7}}-frac{6}{sqrt{7}-2}-frac{sqrt{7}-5}{2}right)c/left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}d/frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
Đọc tiếp
Tính
a/\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
b/\(\left(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\right)\)
c/\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
d/\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
Rút gọn :
1, sqrt{8}-3sqrt{32}+sqrt{72}
2, 6sqrt{12}-sqrt{20}-2sqrt{27}+sqrt{125}
3 , 3sqrt{112}-7sqrt{216}+4sqrt{54}-2sqrt{252}-3sqrt{96}
4, 3sqrt{3}left(3+2sqrt{6}-sqrt{33}right)
6, sqrt{2}left(sqrt{8}-sqrt{32}+3sqrt{18}right)
7, (5sqrt{6}-4sqrt{10}+7sqrt{30}):sqrt{2}
8, left(2sqrt{28}-3sqrt{7}+5sqrt{63}right)sqrt{112}
9, left(5sqrt{3}+3sqrt{5}right):sqrt{15}
10, left(4sqrt{27}-2sqrt{48}-5sqrt{75}right):2sqrt{3}
11, left(1+sqrt{3}-sqrt{2}right).left(1+sqrt{3}+sqrt{2}right)
các bạn...
Đọc tiếp
Rút gọn :
1, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)
2, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
3 , \(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
4, \(3\sqrt{3}\left(3+2\sqrt{6}-\sqrt{33}\right)\)
6, \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
7, \((5\sqrt{6}-4\sqrt{10}+7\sqrt{30}):\sqrt{2}\)
8, \(\left(2\sqrt{28}-3\sqrt{7}+5\sqrt{63}\right)\sqrt{112}\)
9, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
10, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
11, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
các bạn ơi ! giúp mik với đi !
Thực hiện phép tính:a)left(frac{2sqrt{3}-sqrt{6}}{sqrt{8}-2}-frac{sqrt{216}}{3}right).frac{1}{sqrt{6}}b) left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}c) frac{sqrt{5-2sqrt{6}}+sqrt{8-2sqrt{15}}}{sqrt{7+2sqrt{10}}}d) left(sqrt{28}-2sqrt{14}+sqrt{7}right).sqrt{7}+7sqrt{8}
Đọc tiếp
Thực hiện phép tính:
a)\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c) \(\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
d) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
Thêm câu này hộ tớ nx nhé !
e) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right).\left(\sqrt{2}-3\sqrt{0.4}\right)\)
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\(a,\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{12}-\sqrt{6}}{2\left(\sqrt{2}-1\right)}-\frac{6\sqrt{6}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-2\sqrt{6}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}}{2}-\frac{4\sqrt{6}}{2}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{\sqrt{6}-4\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{-3\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=-\frac{3}{2}\)
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\(b,\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
\(=\left(\frac{\sqrt{7}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}+\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\right).\left(\sqrt{7}-\sqrt{5}\right)\)
\(=\left(\frac{-\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\right).\left(\sqrt{7}-\sqrt{5}\right)\)
\(=\left(-\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(7-5\right)\)
\(=-2\)
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Bài 1 : rút gọn
a, sqrt{8}-3sqrt{32}+sqrt{72}
b, 6sqrt{12}-sqrt{20}-2sqrt{27}+sqrt{125}
c, 3sqrt{112}-7sqrt{216}+4sqrt{54}-2sqrt{252}-3sqrt{96}
bài 2 : rút gọn
1, 3sqrt{3}left(3+2sqrt{6}-sqrt{33}right)
2, sqrt{2}left(sqrt{8}-sqrt{32}+3sqrt{18}right)
3, left(2sqrt{2}-3sqrt{7}+5sqrt{63}right)sqrt{112}
4, (5sqrt{6}-4sqrt{10}+7sqrt{30}):sqrt{2}
5, left(5sqrt{3}+3sqrt{5}right):sqrt{15}
6, left(4sqrt{27}-2sqrt{48}-5sqrt{75}right):2sqrt{3}
7, left(1+sqrt{3}-sqrt{2}right).left(1+sqrt{3}+sqr...
Đọc tiếp
Bài 1 : rút gọn
a, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)
b, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
c, \(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
bài 2 : rút gọn
1, \(3\sqrt{3}\left(3+2\sqrt{6}-\sqrt{33}\right)\)
2, \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
3, \(\left(2\sqrt{2}-3\sqrt{7}+5\sqrt{63}\right)\sqrt{112}\)
4, \((5\sqrt{6}-4\sqrt{10}+7\sqrt{30}):\sqrt{2}\)
5, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
6, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
7, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
các bạn ơi ! giúp mik vs đi !!!!!!!!!!!!!!
tính
\(\sqrt{5}.\left(\sqrt{3}+\sqrt{2}\right)\)
\(\left(\sqrt{3}-\sqrt{5}\right)^2\)
\(\left(\sqrt{7}-\sqrt{2}\right).\left(\sqrt{7}+\sqrt{2}\right)\)
\(\left(\sqrt{3}+\sqrt{5}\right)^2\)
\(\left(\sqrt{8+3\sqrt{7}}\right)+\left(\sqrt{8-3\sqrt{7}}\right)\)
