二次根式计算题30道带答案
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1/6√1又3/5×(-5√3又√3/5)
=1/6√(8/5)×(-5/3√(3/5)
=-5/18√(24/25)
=-5/18×2/5√6
=-1/9√6
(2)√8/a×√2a/b
=√(8/a×2a/b)
=√(16/b)
=4/b(√b)
(3)√2x乘以√2y乘以√x
=√(2x*2y*x)
=2x√y
(4)2√a÷4√b
=√a/2√b
=1/2b√ab
(5)5√xy÷√5x^3
=5√(xy/5x³)
=1/x√5y
(6)√x-y÷√x+y
=1/(x+y)√(x²-y²)
(7)√x(x+y)÷√xy^2/x+y(x>0,y>0)
=√[x(x+y)÷xy²/(x+y)]
=(x+y)/y
(8)√xy乘以√6x÷√3y
=√6x²y÷√3y
=x√2
(9)(√mn-√m/n)÷√m/n(n>0)
=√mn÷m/n-√m/n÷m/n
=n-1(10)√3/8-(-3/4√27/2+3√1/6)
=1/4√6+3/8√6-1/2√6
=1/8√6
(11)2/3√9x+6√x/4-2x√1/x
=2√3x+3/2√x-2√x
=5/2√x
(12)2/a√4a+√1/a-2a√1/a^3
=1/a√a+1/a√a-2/a√a
=0
(13)√0.2m+1/m√5m^3-m√125/m
=1/5√5m+√5m-5√5m
=-19/5√5m
(14)√a+b/a-b-√a-b/a+b-√1/a^2-b^2(a>b>0)
=1/(a-b)√(a²-b²)-1/(a+b)√(a²-b²)-1/(a²-b²)√(a²-b²)
=(a+b-a+b-1)/(a²-b²)√(a²-b²)
=(2b+1)/(a²-b²)√(a²-b²)
解不等式
(15)2x+√32<x+√2
2x-x<√2-4√2
x<-3√216)√3/8-(-3/4√27/2+3√1/6)
=1/2√3/2 + 9/4√3/2 - 1/2√6
=1/4√6 + 9/8√6 - 1/2√6
=7/8√6
(17)√0.2m+1/m√5m^3-m√125/m
=√1/5*m + 1/m√5m*m^2 - m√25*5m/m^2
=1/5√5m+√5m-5√5m
=-19/5√5m
(18)(√45+√27)+(√1又1/3-√125)
=3√5+3√3 + √4/3-5√5
=3√3 + 2/3√3 + 3√5 - 5√5
=5√3 -2√5
(19)2/3√9x+6√x/4-2x√1/x
=2√x+3√x-2√x
=3√x
20 √40÷√5
=√8*√5÷√5
=√8
=2√2
21 √32/√2
=√16*√2/√2
=√16
=4
22 √4/5÷√2/15
=√4/5*√15/2
=√(4/5*15/2)
=√6
23 2√a^3b/√ab
=2√a²√ab/√ab
=2√a²
=2|a|(24)√18-√32+√2
=√2×9-√4×4×2+√2
=3√2-4√2+√2
=0
(25)√75-√54+√96-√108
=√5×5×3-√6×3×3+√6×4×4-√3×6×6
=5√3-3√6+4√6-6√3
=√6-√3
=√3(√2-1)
(26)(√45+√18)-(√8-√125)
=√5×3×3+√2×3×3-√2×2×2+√5×5×5
=3√5+3√2-3√2+5√5
=8√5
(27)½(√2+√3)-¾(√2+√27)
=¼(2√2+2√3-√2-√27)此处通分,分子不变,分母都分别乘进去了,因为不好写就省略了
=¼(2√2+2√3-√2-√3×3×3)
=¼(√2-√3)
(28)¼根号下18ab×(-2/b根号下6a²/a)
=1/4×(-2/b)×√(18ab×6a²/a)
=-1/(2b)×3a√(2b)
=-3a/(2b) √(2b)
(29)根号下50a²b(a<0,b>0)
=√(25a²×2b)
=-5a√(2b)
(30)根号18×3/2根号20×(-1/3根号15)
=-1/3×3/2×√(18×20×15)
=-1/2×√5400
=-1/2×30√6
=-15√6
=1/6√(8/5)×(-5/3√(3/5)
=-5/18√(24/25)
=-5/18×2/5√6
=-1/9√6
(2)√8/a×√2a/b
=√(8/a×2a/b)
=√(16/b)
=4/b(√b)
(3)√2x乘以√2y乘以√x
=√(2x*2y*x)
=2x√y
(4)2√a÷4√b
=√a/2√b
=1/2b√ab
(5)5√xy÷√5x^3
=5√(xy/5x³)
=1/x√5y
(6)√x-y÷√x+y
=1/(x+y)√(x²-y²)
(7)√x(x+y)÷√xy^2/x+y(x>0,y>0)
=√[x(x+y)÷xy²/(x+y)]
=(x+y)/y
(8)√xy乘以√6x÷√3y
=√6x²y÷√3y
=x√2
(9)(√mn-√m/n)÷√m/n(n>0)
=√mn÷m/n-√m/n÷m/n
=n-1(10)√3/8-(-3/4√27/2+3√1/6)
=1/4√6+3/8√6-1/2√6
=1/8√6
(11)2/3√9x+6√x/4-2x√1/x
=2√3x+3/2√x-2√x
=5/2√x
(12)2/a√4a+√1/a-2a√1/a^3
=1/a√a+1/a√a-2/a√a
=0
(13)√0.2m+1/m√5m^3-m√125/m
=1/5√5m+√5m-5√5m
=-19/5√5m
(14)√a+b/a-b-√a-b/a+b-√1/a^2-b^2(a>b>0)
=1/(a-b)√(a²-b²)-1/(a+b)√(a²-b²)-1/(a²-b²)√(a²-b²)
=(a+b-a+b-1)/(a²-b²)√(a²-b²)
=(2b+1)/(a²-b²)√(a²-b²)
解不等式
(15)2x+√32<x+√2
2x-x<√2-4√2
x<-3√216)√3/8-(-3/4√27/2+3√1/6)
=1/2√3/2 + 9/4√3/2 - 1/2√6
=1/4√6 + 9/8√6 - 1/2√6
=7/8√6
(17)√0.2m+1/m√5m^3-m√125/m
=√1/5*m + 1/m√5m*m^2 - m√25*5m/m^2
=1/5√5m+√5m-5√5m
=-19/5√5m
(18)(√45+√27)+(√1又1/3-√125)
=3√5+3√3 + √4/3-5√5
=3√3 + 2/3√3 + 3√5 - 5√5
=5√3 -2√5
(19)2/3√9x+6√x/4-2x√1/x
=2√x+3√x-2√x
=3√x
20 √40÷√5
=√8*√5÷√5
=√8
=2√2
21 √32/√2
=√16*√2/√2
=√16
=4
22 √4/5÷√2/15
=√4/5*√15/2
=√(4/5*15/2)
=√6
23 2√a^3b/√ab
=2√a²√ab/√ab
=2√a²
=2|a|(24)√18-√32+√2
=√2×9-√4×4×2+√2
=3√2-4√2+√2
=0
(25)√75-√54+√96-√108
=√5×5×3-√6×3×3+√6×4×4-√3×6×6
=5√3-3√6+4√6-6√3
=√6-√3
=√3(√2-1)
(26)(√45+√18)-(√8-√125)
=√5×3×3+√2×3×3-√2×2×2+√5×5×5
=3√5+3√2-3√2+5√5
=8√5
(27)½(√2+√3)-¾(√2+√27)
=¼(2√2+2√3-√2-√27)此处通分,分子不变,分母都分别乘进去了,因为不好写就省略了
=¼(2√2+2√3-√2-√3×3×3)
=¼(√2-√3)
(28)¼根号下18ab×(-2/b根号下6a²/a)
=1/4×(-2/b)×√(18ab×6a²/a)
=-1/(2b)×3a√(2b)
=-3a/(2b) √(2b)
(29)根号下50a²b(a<0,b>0)
=√(25a²×2b)
=-5a√(2b)
(30)根号18×3/2根号20×(-1/3根号15)
=-1/3×3/2×√(18×20×15)
=-1/2×√5400
=-1/2×30√6
=-15√6
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