Rút gọn: \(3\sqrt{12}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}.\)
Những câu hỏi liên quan
1) sqrt{12}-sqrt{27}+sqrt{3}
2)sqrt{252}-sqrt{700}+sqrt{1008}-sqrt{448}
3)3sqrt{112}-7sqrt{216}+4sqrt{54}-2sqrt{252}-3sqrt{96}
4)sqrt{18}-3sqrt{80}-2sqrt{50}+2sqrt{45}
5)6sqrt{12}-sqrt{20}-2sqrt{27}+sqrt{125}
6)2sqrt{18}-3sqrt{80}-5sqrt{147}+5sqrt{245}-3sqrt{98}
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1) \(\sqrt{12}-\sqrt{27}+\sqrt{3}\)
2)\(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
3)\(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
4)\(\sqrt{18}-3\sqrt{80}-2\sqrt{50}+2\sqrt{45}\)
5)\(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
6)\(2\sqrt{18}-3\sqrt{80}-5\sqrt{147}+5\sqrt{245}-3\sqrt{98}\)
GIÚP MÌNH VỚI
Ối giời! Bấm máy tính đi bn! Người ta sinh ra cái máy tính là để làm mấy việc này mà. :D
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\(1.\sqrt{12}-\sqrt{27}+\sqrt{3}\\ =2\sqrt{3}-3\sqrt{3}+\sqrt{3}\\ =0\)
\(2.\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\\ =6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}\\ =0\)
\(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\\ =12\sqrt{7}-42\sqrt{6}+12\sqrt{6}-12\sqrt{7}-12\sqrt{6}\\ =-42\sqrt{6}\)
\(4.\sqrt{18}-3\sqrt{80}-2\sqrt{50}+2\sqrt{45}\\ =3\sqrt{2}-12\sqrt{5}-10\sqrt{2}+6\sqrt{5}\\ =-7\sqrt{2}-6\sqrt{5}\)
\(5.6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\\ =12\sqrt{3}-2\sqrt{5}-6\sqrt{3}+5\sqrt{5}\\ =6\sqrt{3}+3\sqrt{5}\)
\(6.2\sqrt{18}-3\sqrt{80}-5\sqrt{147}+5\sqrt{245}-3\sqrt{98}\\ =6\sqrt{2}-12\sqrt{5}-35\sqrt{3}+35\sqrt{5}-21\sqrt{2}\\ =-15\sqrt{2}-35\sqrt{3}+23\sqrt{5}\)
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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...
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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 !!!!!!!!!!!!!!
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 !
Rút gọn các biểu thức :
a) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)
b) \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
c)\(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
a: \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)
\(=4-\sqrt{15}+\sqrt{15}=4\)
b: \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(=2+\sqrt{3}-2+\sqrt{3}\)
\(=2\sqrt{3}\)
c: \(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(=\sqrt{\left(2\sqrt{5}+3\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}\)
\(=2\sqrt{5}+3-2\sqrt{5}+3=6\)
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Rút gọn các biểu thức sau: 9, A sqrt{4+sqrt{15}}-sqrt{7-3sqrt{5}}10, A sqrt{2+sqrt{3}}+sqrt{2-sqrt{3}}11, A text{}text{}text{}sqrt{12-3sqrt{7}}-sqrt{12+3sqrt{7}}12, A left(3sqrt{2}+sqrt{6}right)sqrt{6-3sqrt{3}}13, A sqrt{9-4sqrt{5}}-sqrt{14-6sqrt{5}}
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Rút gọn các biểu thức sau:
9, A = \(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
10, A = \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
11, A = \(\text{}\text{}\text{}\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
12, A = \(\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\)
13, A = \(\sqrt{9-4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
9: \(A=\dfrac{\sqrt{8+2\sqrt{15}}-\sqrt{14-6\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}-3+\sqrt{5}}{\sqrt{2}}=\dfrac{2\sqrt{10}+\sqrt{6}-3\sqrt{2}}{2}\)
10: \(A=\dfrac{\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1+\sqrt{3}-1}{\sqrt{2}}=\dfrac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\)
11: \(A=\dfrac{\sqrt{24-6\sqrt{7}}-\sqrt{24+6\sqrt{7}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{21}-\sqrt{3}-\sqrt{21}-\sqrt{3}}{\sqrt{2}}=-\dfrac{2\sqrt{3}}{\sqrt{2}}=-\sqrt{6}\)
12: \(B=\left(3+\sqrt{3}\right)\sqrt{12-6\sqrt{3}}\)
\(=\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)\)
=9-3=6
13: \(A=\sqrt{5}-2-\left(3-\sqrt{5}\right)\)
\(=\sqrt{5}-2-3+\sqrt{5}=2\sqrt{5}-5\)
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Rút gọn biểu thức
M = \(\dfrac{2}{\sqrt{7}-\sqrt{6}}-\sqrt{28}+\sqrt{54}\)
N= \(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
a) Ta có: \(M=\dfrac{2}{\sqrt{7}-\sqrt{6}}-\sqrt{28}+\sqrt{54}\)
\(=\dfrac{2\left(\sqrt{7}+\sqrt{6}\right)}{\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right)}-2\sqrt{7}+3\sqrt{6}\)
\(=2\sqrt{7}+2\sqrt{6}-2\sqrt{7}+3\sqrt{6}\)
\(=5\sqrt{6}\)
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b) Ta có: \(N=\left(2-\sqrt{3}\right)\left(\sqrt{26+15\sqrt{3}}\right)-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{52+30\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{52-30\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{27+2\cdot3\sqrt{3}\cdot5+25}-\left(2+\sqrt{3}\right)\sqrt{27-2\cdot3\sqrt{3}\cdot5+25}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{\left(3\sqrt{3}+5\right)^2}-\left(2+\sqrt{3}\right)\sqrt{\left(3\sqrt{3}-5\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\left(3\sqrt{3}+5\right)-\left(2+\sqrt{3}\right)\left(3\sqrt{3}-5\right)}{\sqrt{2}}\)
\(=\dfrac{6\sqrt{3}+10-9-5\sqrt{3}-\left(6\sqrt{3}-10+9-5\sqrt{3}\right)}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1-\sqrt{3}+1}{\sqrt{2}}\)
\(=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
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Rút gọn các biểu thức saua) dfrac{1}{sqrt{3}}+dfrac{1}{3sqrt{2}}+dfrac{1}{sqrt{3}}dfrac{sqrt{3}-sqrt{2}}{2sqrt{3}} b) sqrt{12-3sqrt{7}}-sqrt{12+3sqrt{7}} c) sqrt[3]{dfrac{3}{4}}.sqrt[3]{dfrac{9}{16}}d) dfrac{sqrt[3]{54}}{sqrt[3]{-2}} e) sqrt[3]{5sqrt{2}+7}-sqrt[3]{5sqrt{2}-7}
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Rút gọn các biểu thức sau
a) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\dfrac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}\) b) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\) c) \(\sqrt[3]{\dfrac{3}{4}}.\sqrt[3]{\dfrac{9}{16}}\)
d) \(\dfrac{\sqrt[3]{54}}{\sqrt[3]{-2}}\) e) \(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
b) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
\(=\dfrac{\sqrt{2}\cdot\sqrt{12-3\sqrt{7}}-\sqrt{2}\cdot\sqrt{12+3\sqrt{7}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{24-6\sqrt{7}}-\sqrt{24+6\sqrt{7}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{21}\right)^2-2\cdot\sqrt{21}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{21}\right)^2+2\cdot\sqrt{21}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{21}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{21}+\sqrt{3}\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{21}-\sqrt{3}-\sqrt{21}-\sqrt{3}}{\sqrt{2}}\)
\(=\dfrac{-2\sqrt{3}}{\sqrt{2}}\)
\(=-\sqrt{6}\)
c) \(\sqrt[3]{\dfrac{3}{4}}\cdot\sqrt[3]{\dfrac{9}{16}}\)
\(=\sqrt[3]{\dfrac{3\cdot9}{4\cdot16}}\)
\(=\sqrt[3]{\left(\dfrac{3}{4}\right)^3}\)
\(=\dfrac{3}{4}\)
d) \(\dfrac{\sqrt[3]{54}}{\sqrt[3]{-2}}\)
\(=\sqrt[3]{\dfrac{54}{-2}}\)
\(=\sqrt[3]{-27}\)
\(=\sqrt[3]{\left(-3\right)^3}\)
\(=-3\)
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a: Sửa đề: \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\cdot\dfrac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}\)
\(=\dfrac{1}{\sqrt{3}}+\dfrac{1}{\sqrt{3}\cdot\sqrt{6}}+\dfrac{\sqrt{3}-\sqrt{2}}{12}\)
\(=\dfrac{\sqrt{6}+1}{3\sqrt{2}}+\dfrac{\sqrt{3}-\sqrt{2}}{12}\)
\(=\dfrac{2\sqrt{2}\left(\sqrt{6}+1\right)+\sqrt{3}-\sqrt{2}}{12}\)
\(=\dfrac{4\sqrt{3}+2\sqrt{2}+\sqrt{3}-\sqrt{2}}{12}\)
\(=\dfrac{5\sqrt{3}+\sqrt{2}}{12}\)
e: \(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
\(=\sqrt[3]{2\sqrt{2}+3\sqrt{2}+6+1}-\sqrt[3]{2\sqrt{2}-3\sqrt{2}+6-1}\)
\(=\sqrt[3]{\left(\sqrt{2}+1\right)^3}-\sqrt[3]{\left(\sqrt{2}-1\right)^3}\)
\(=\sqrt{2}+1-\left(\sqrt{2}-1\right)\)
\(=\sqrt{2}+1-\sqrt{2}+1=2\)
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Thực hiện phép tính (rút gọn biểu thức)
a)\(\sqrt{20}\)-3\(\sqrt{45}\)-\(\dfrac{1}{2}\sqrt{80}\)
b) 12\(\sqrt{54}\)-\(\dfrac{2}{5}\)\(\sqrt{150}\)+3\(\sqrt{24}\)
Lời giải:
a.
$=2\sqrt{5}-9\sqrt{5}-2\sqrt{5}=(2-9-2)\sqrt{5}=-9\sqrt{5}$
b.
$=36\sqrt{6}-2\sqrt{6}+6\sqrt{6}=(36-2+6)\sqrt{6}=40\sqrt{6}$
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Rút gọn các biểu thức sau : a) sqrt{18left(sqrt{2}-sqrt{3}right)^2} - sqrt{54}b) dfrac{a+sqrt{ab}}{sqrt{a}-sqrt{b}} - asqrt{dfrac{1}{a}}c) ( sqrt{28} - 2sqrt{3} +7) sqrt{7} +sqrt{84}
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Rút gọn các biểu thức sau :
a) \(\sqrt{18\left(\sqrt{2}-\sqrt{3}\right)^2}\) - \(\sqrt{54}\)
b) \(\dfrac{a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\) - a\(\sqrt{\dfrac{1}{a}}\)
c) ( \(\sqrt{28}\) - 2\(\sqrt{3}\) +7) \(\sqrt{7}\) +\(\sqrt{84}\)
a: \(=3\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)-3\sqrt{6}\)
=3căn 6-6-3căn 6=-6
b: \(=\dfrac{a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\sqrt{a}\)
\(=\dfrac{a+\sqrt{ab}-a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}=\dfrac{2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\)
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