1.(√2 + 1)^3 − (√2 − 1)^3
2.√13 − √160 − √53 + 4√90
3.(√3 + 1)^3 − (√3 − 1)^3
Những câu hỏi liên quan
a/ (√10+√2) (6-2√5)√(3+√5)
b/ √(13-√160) - √(53-4√90)
c/ √(10+√24+√40+√60)
d/ (√2+√3+√6+√8+√16)/(√2+√3+√4)
e/ [√216/3-(2√3-√6)/(√8-2)] ×1/√6
f/ 1/(√2-√3) × √[(3√2-2√3)/(3√2+2√3)]
g/ 1/(√1+√2) + 1/(√2+√3) + ......+ 1/(√2017+√2018)
Thực hiện phép tính
a, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
b,\(\left(1+\sqrt{3}-\sqrt{2}\right)\cdot\left(1+\sqrt{3}+\sqrt{2}\right)\)
a) \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
\(=\sqrt{13-2\sqrt{40}}-\sqrt{53+12\sqrt{10}}\)
\(=\sqrt{\left(\sqrt{8}\right)^2-2.\sqrt{8}.\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{5}\right)^2+2.3\sqrt{5}.2\sqrt{2}+\left(2\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{8}-\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{5}+2\sqrt{2}\right)^2}\)
\(=\left|\sqrt{8}-\sqrt{5}\right|-\left|3\sqrt{5}+2\sqrt{2}\right|\)
= √8 - √5 - 3√5 - 2√2 = -4√5
b) (1+√3-√2).(1+√3+√2)= [(1+√3)^2-(√2)^2] = 4+2√3-2=2+2√3
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a) =sprt{13-=sprt{160}} - =sprt{53+4=sprt{90}}
= =sprt{(=sprt{8} - =sprt{5})2 } - =sprt{(=sprt{45} + =sprt{8})2 }
= =sprt{8} - =sprt{5} - =sprt{45} - =sprt{8}
= -3=sprt{5}
b) ( 1 + =sprt{3} - =sprt{2} )( 1+ =sprt{3} + =sprt{2} )
= ( 1 + =sprt{3} )2 - (=sprt{2})2
= 4 + 2=sprt{3} - 2
=2 + 2=sprt{3}
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1. √(9-4√5) - √(14+6√5)
2.(3√2+√10) +√(28-12√5)
3.√(4+2√3)× √(√3 - 1) 2
4. √(13-√160)-√(53+4√60)
1. \(\sqrt{\left(9-4\sqrt{5}\right)}\) - \(\sqrt{\left(14+6\sqrt{5}\right)}\) = \(\sqrt{5+4-2\cdot2\sqrt{5}}\) - \(\sqrt{9+5+2\cdot3\sqrt{5}}\) = \(\sqrt{\left(2-\sqrt{5}\right)^2}\) - \(\sqrt{\left(3+\sqrt{5}\right)^2}\) = \(\sqrt{5}-2\) - \(3-\sqrt{5}\) = -5
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1: \(=\sqrt{5}-2-3-\sqrt{5}=-5\)
2: \(=3\sqrt{2}+\sqrt{10}+3\sqrt{2}-\sqrt{10}=6\sqrt{2}\)
4: \(=2\sqrt{2}-\sqrt{5}-4\sqrt{3}-\sqrt{5}=2\sqrt{2}-4\sqrt{3}-2\sqrt{5}\)
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A= 13/30 + 28/45∙ 2 1/2 -[(1/2+1/3): 53/90]: 50/53
1. √(9-4√5) - √(14+6√5)
2. (3√2 + √10) + √(28-12√5)
3. √(13-√160) - √(53+4√60)
1: \(=\sqrt{5}-2-3-\sqrt{5}=-5\)
2: \(=3\sqrt{2}+\sqrt{10}+3\sqrt{2}-\sqrt{10}=6\sqrt{2}\)
3: \(=2\sqrt{2}-\sqrt{5}-4\sqrt{3}-\sqrt{5}=2\sqrt{2}-4\sqrt{3}-2\sqrt{5}\)
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1. √(9-4√5) - √(14+6√5)
2. (3√2 + √10) + √(28-12√5)
3. √(13-√160) - √(53+4√60)
1: \(=\sqrt{5}-2-3-\sqrt{5}=-5\)
2: \(=3\sqrt{2}+\sqrt{10}+3\sqrt{2}-\sqrt{10}=6\sqrt{2}\)
3: \(=2\sqrt{2}-\sqrt{5}-4\sqrt{3}-\sqrt{5}=2\sqrt{2}-4\sqrt{3}-2\sqrt{5}\)
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Thực hiện phép tinh:
a)\(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
b) \(2\sqrt{3}.\left(\sqrt{27}+2\sqrt{48}-\sqrt{75}\right)\)
c) \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
d) \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
a/\(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
\(=2\sqrt{3}+6\sqrt{3}+15\sqrt{3}-36\sqrt{3}=-13\sqrt{3}\)
b/ \(2\sqrt{3}\left(\sqrt{27}+2\sqrt{48}-\sqrt{75}\right)\)
\(=2\sqrt{3}\left(3\sqrt{3}+8\sqrt{3}-5\sqrt{3}\right)\)
\(=2\sqrt{3}\cdot6\sqrt{3}=2\cdot6\cdot3=36\)
c/ \(\left(1+\sqrt{3}-\sqrt{2}\right)\left(1+\sqrt{3}+\sqrt{2}\right)\)
\(=\left(1+\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\)
\(=1+2\sqrt{3}+3-2\)
\(=2+2\sqrt{3}\)
d/ \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
\(=\sqrt{13-4\sqrt{10}}-\sqrt{53+4\sqrt{90}}\)
\(=\sqrt{8-4\sqrt{10}+5}-\sqrt{45+12\sqrt{10}+8}\)
\(=\sqrt{\left(2\sqrt{2}\right)^2-2\cdot2\sqrt{2\cdot5}+\left(\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{5}\right)^2+2\cdot3\cdot2\sqrt{5\cdot2}+\left(2\sqrt{2}\right)^2}\)
\(=\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{5}+2\sqrt{2}\right)^2}\)
\(=2\sqrt{2}-\sqrt{5}-3\sqrt{5}-2\sqrt{2}\)
\(=-4\sqrt{5}\)
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#)Giải :
\(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}=2\sqrt{3}+6\sqrt{3}+15\sqrt{3}-36\sqrt{3}=-13\sqrt{3}\)
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1. Tính
a, 1+7+8+15+23+...+160
b, 17+4+5+9+19+...+60+9
c, 78*3+78*24+78*17*22*72
d, 53*39+47*39+47-53*21-47*21
e, 2*53*12+4*6*87-3*8*40
g, 5*7*77-7*60+49*25-15*42
h, 1*2+2*3+3*4+...+2016*2017
⛇3/8+3/4 3/4 nhân12
1/6-1/12 13/7-9/5
3/8:2
\(\dfrac{3}{8}+\dfrac{3}{4}=\dfrac{3+3\cdot2}{8}=\dfrac{9}{8}\)
\(\dfrac{3}{4}\cdot12=\dfrac{3\cdot12}{4}=\dfrac{36}{4}=9\)
\(\dfrac{1}{6}-\dfrac{1}{12}=\dfrac{2}{12}-\dfrac{1}{12}=\dfrac{1}{12}\)
\(\dfrac{13}{7}-\dfrac{9}{5}=\dfrac{13\cdot5-9\cdot7}{7\cdot5}=\dfrac{2}{35}\)
\(\dfrac{3}{8}:2=\dfrac{3}{8\cdot2}=\dfrac{3}{16}\)
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