最新数学初二基础知识点实数

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√3 X-1=√2 X

求X

{√5 X-3√ Y=1}

{√3 X-√5 Y=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√5 2.=√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).