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13 tháng 6 2019
\(A=2\sqrt{5}-\sqrt{45}+2\sqrt{20}=2\sqrt{5}-\sqrt{3^2.5}+2\sqrt{2^2.5}=2\sqrt{5}-3\sqrt{5}+4\sqrt{5}=3\sqrt{5}\)
\(B=\left(\sqrt{18}-\frac{1}{2}\cdot\sqrt{32}+12\sqrt{2}\right):\sqrt{2}=\left(3\sqrt{2}-\frac{1}{2}\cdot4\sqrt{2}+12\sqrt{2}\right):\sqrt{2}\)
\(=13\sqrt{2}:\sqrt{2}=13\)
\(C=\left(\sqrt{12}+2\sqrt{27}-3\sqrt{3}\right)\cdot\sqrt{3}=\left(2\sqrt{3}+6\sqrt{3}-3\sqrt{3}\right)\cdot\sqrt{3}=5\sqrt{3}\cdot\sqrt{3}=15\)
\(D=\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}=2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}=-\sqrt{5}+15\sqrt{2}\)
12 tháng 9 2021
Ta có: \(b=\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
\(=\dfrac{2\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}{3\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}\)
\(=\dfrac{2}{3}\)
Ta có: \(a=\sqrt{4+2\sqrt{2}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2-\sqrt{2}}\)
\(=\sqrt{2\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\)
=2
Thay a=2 và \(b=\dfrac{2}{3}\) vào M, ta được:
\(M=\dfrac{1+2\cdot\dfrac{2}{3}}{2+\dfrac{2}{3}}-\dfrac{1-2\cdot\dfrac{2}{3}}{2-\dfrac{2}{3}}\)
\(=\dfrac{7}{8}+\dfrac{1}{4}\)
\(=\dfrac{7}{8}+\dfrac{2}{8}=\dfrac{9}{8}\)
27 tháng 7 2023
a: \(=3\sqrt{5}+2\sqrt{5}-2\sqrt{5}=3\sqrt{5}\)
b: \(=2\sqrt{2}+2\sqrt{2}+5\sqrt{2}=9\sqrt{2}\)
c: \(=4\sqrt{3}+3\sqrt{3}-3\sqrt{5}+2\sqrt{5}=7\sqrt{3}-\sqrt{5}\)
d: \(=5\sqrt{3}+4\sqrt{3}-10\sqrt{3}=-\sqrt{3}\)
e: \(=\left(\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\)
=7-2*căn 21+2*căn 21
=7
f: \(=\left(2\sqrt{11}-3\sqrt{2}\right)\cdot\sqrt{11}+3\sqrt{22}\)
=22-3*căn 22+3*căn 22
=22
H9
HT.Phong (9A5)
CTVHS
27 tháng 7 2023
a) \(3\sqrt{5}+\sqrt{20}-2\sqrt{5}\)
\(=3\sqrt{5}+2\sqrt{5}-2\sqrt{5}\)
\(=3\sqrt{5}\)
b) \(2\sqrt{2}+\sqrt{8}+\sqrt{50}\)
\(=2\sqrt{2}+2\sqrt{2}+5\sqrt{2}\)
\(=9\sqrt{5}\)
c) \(4\sqrt{3}+\sqrt{27}-\sqrt{45}+2\sqrt{5}\)
\(=4\sqrt{3}+3\sqrt{3}-3\sqrt{5}+2\sqrt{5}\)
\(=7\sqrt{3}-\sqrt{5}\)
d) \(\sqrt{75}+\sqrt{48}-\sqrt{300}\)
\(=5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\)
\(=-\sqrt{3}\)
e) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
\(=\left(2\sqrt{7}-2\sqrt{3}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
\(=\left(\sqrt{7}-2\sqrt{3}\right)\sqrt{7}+2\sqrt{21}\)
\(=7-2\sqrt{21}+2\sqrt{21}\)
\(=7\)
f) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(=\left(3\sqrt{11}-3\sqrt{2}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(=\left(2\sqrt{11}-3\sqrt{2}\right)\sqrt{11}+3\sqrt{22}\)
\(=22-3\sqrt{22}+3\sqrt{22}\)
\(=22\)
g) \(3\sqrt{45}-5\sqrt{125x}+7\sqrt{20x}+28\)
\(=9\sqrt{5}-25\sqrt{5x}+14\sqrt{5x}+28\)
\(=9\sqrt{5}-11\sqrt{5x}+28\)
H
3 tháng 11 2023
\(\left(\sqrt{12}+\sqrt{27}-\sqrt{18}\right)\cdot3\\ =(\sqrt{4\cdot3}+\sqrt{9\cdot3}-\sqrt{6}\cdot\sqrt{3})\cdot\sqrt{3}\\ =\left(2\sqrt{3}+3\sqrt{3}-\sqrt{6}\cdot\sqrt{3}\right)\cdot\sqrt{3}\\ =2\cdot3+3\cdot3-\sqrt{6}\cdot3\\ =6+9-3\sqrt{6}\\ =15-3\sqrt{6}\)
\(\left(15\sqrt{20}-3\sqrt{45}+2\sqrt{5}\right):\sqrt{5}\\ =\left(15\sqrt{4\cdot5}-3\sqrt{9\cdot5}+2\sqrt{5}\right):\sqrt{5}\\ =\left(30\sqrt{5}-9\sqrt{5}+2\sqrt{5}\right):\sqrt{5}\\ =30-9+2\\ =23\)
17 tháng 5 2021
`a)A=\sqrt{4+2sqrt3}`
`=\sqrt{3+2sqrt3+1}`
`=sqrt{(sqrt3+1)^2}`
`=sqrt3+1`
`B)1/(2-sqrt3)+1/(2+sqrt3)`
`=(2+sqrt3)/(4-3)+(2-sqrt3)/(4-3)`
`=2+sqrt3+2-sqrt3`
`=4`
`\sqrt{4x-12}+sqrtx{x-3}-1/3sqrt{9x-27}=8`
`đk:x>=3`
`pt<=>2sqrt{x-3}+sqrt{x-3}-sqrt{x-3}=8`
`<=>2sqrt{x-3}=8`
`<=>sqrt{x-3}=4`
`<=>x-3=16`
`<=>x=19`
Vậy `S={19}`
17 tháng 5 2021
`a)A=\sqrt{4+2sqrt3}`
`=\sqrt{3+2sqrt3+1}`
`=sqrt{(sqrt3+1)^2}`
`=sqrt3+1`
`B)1/(2-sqrt3)+1/(2+sqrt3)`
`=(2+sqrt3)/(4-3)+(2-sqrt3)/(4-3)`
`=2+sqrt3+2-sqrt3`
`=4`
`\sqrt{4x-12}+sqrt{x-3}-1/3sqrt{9x-27}=8`
`đk:x>=3`
`pt<=>2sqrt{x-3}+sqrt{x-3}-sqrt{x-3}=8`
`<=>2sqrt{x-3}=8`
`<=>sqrt{x-3}=4`
`<=>x-3=16`
`<=>x=19`
Vậy `S={19}`