关于初二年级数学知识点的梳理

1.被开方数含有平方因数：分解因数(准确找到平方因数)

2.被开方数含有分母：分母变成平方数

解方程√3X-1=√2X

求X

{√5X-3√Y=1}

{√3X-√5Y=2}

注：X全部不在根号内

√(1/2x)^2+10/9x^2

=√[1/(4x^2)+10/(9x^2)]

=√49/36x^2

若x>0,=7/(6x)

若x<0,=-7/(6x)

√a^4mb^2n+1

=√(a^2mb^n)^2+1

=a^2mb^n+1

√(4a^5+8a^4)(a^2+3a+2)

=√[4a^4(a+2)][(a+2)(a+1)]

=√[4a^4(a+2)^2(a+1)]

=2a^2(a+2)√(a+1)

.3√(1/6)-4√(50)+30√(2/3)

答案3√(1/6)-4√(50)+30√(2/3)

=3×√6/6-4×5√2+30×√6/3

=√6/2-20√2+10√6

①5√8-2√32+√50=5*3√2-2*4√2+5√2=√2(15-8+5)=12√2

②√6-√3/2-√2/3=√6-√6/2-√6/3=√6/6

③(√45+√27)-(√4/3+√125)=(3√5+3√3)-(2√3/3+5√5)=-2√5+7√5/3

④(√4a-√50b)-2(√b/2+√9a)=(2√a-5√2b)-2(√2b/2+3√a)=-4√a-6√2b

⑤√4x*(√3x/2-√x/6)=2√x(√6x/2-√6x/6)=2√x*(√6x/3)=2/3*x*√6

⑥(x√y-y√x)÷√xy=x√y÷√xy-y√x÷√xy=√x-√y

⑦(3√7+2√3)(2√3-3√7)=(2√3)^2-(3√7)^2=12-63=-51

⑧(√32-3√3)(4√2+√27)=(4√2-3√3)(4√2+3√3)=(4√2)^2-(3√3)^2=32-27=5

⑨(3√6-√4)??=(3√6)^2-2*3√6*√4+(√4)^2=54-12√6+4=58-12√6

⑩(1+√2-√3)(1-√2+√3)=[1+(√2-√3)][1-(√2-√3)]=1-(√2-√3)^2=1-(2+3+2√6)=-4-2√6

1.=5√5-1/25√5-4/5√5=√5*(5-1/25-4/5)=24/5√52.=√144+576=√720=12√5

2.)√(8/13)^2-(2/13)^2=√(8/13+2/13)(8/13-2/13)=(2/13)√15

3.3√(1/6)-4√(50)+30√(2/3)答案3√(1/6)-4√(50)+30√(2/3)=3×√6/6-4×5√2+30×√6/3=√6/2-20√2+10√6

2.(1-根号2)/2乘以(1+根号2)/2题是这样的二分之一减根号2乘以二分之一加根号2答案：(1-根号2)/2乘以(1+根号2)/2=(1-√2)*(1-√2)/4=(1-2)/4=-1/4

3.√(1/2x)^2+10/9x^2√[(1/2x)^2+10/9x^2]=√(x^2/4+10x^2/9)=√(9x^2/36+40x^2/36)=√(49x^2/36)=7x/6;

4.√a^4mb^2n+1(a、b为正数)[√(a^4mb^2n)]+1(a、b为正数)=a^2mb^n+1;

5.√(4a^5+8a^4)(a^2+3a+2)(a>=0)√[(4a^5+8a^4)(a^2+3a+2)](a>=0)=√[4a^4(a+2)(a+2)(a+1)]=√[(2a^2)^2(a+2)^2(a+1)]=2a^2(a+2)√(a+1).