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二次根式计算题100道(二次根式计算题30道带答案)

发布于:2024-06-10 13:04:01 来源:互联网

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

=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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