Matematyka

Autorzy:Drążek Anna, Duvnjak Ewa, Kokiernak-Jurkiewicz Ewa

Wydawnictwo:WSiP

Rok wydania:2016

Wyłącz czynnik przed pierwiastek (x,y,z ≥0). 4.7 gwiazdek na podstawie 10 opinii
  1. Gimnazjum
  2. 2 Klasa
  3. Matematyka

`a) \ \ \ sqrt(12)=sqrt(4*3)=sqrt(4)*sqrt(3)=2sqrt(3)`

`sqrt(28)=sqrt(4*7)=sqrt(4)*sqrt(7)=2sqrt(7)`

`sqrt(44)=sqrt(4*11)=sqrt(4)*sqrt(11)=2sqrt(11)`

`sqrt(80)=sqrt(4*20)=sqrt(4)*sqrt(20)=2sqrt(20)=2sqrt(4*5)=2*sqrt(4)*sqrt(5)=2*2*sqrt(5)=4sqrt(5)`

`sqrt(1/45)=sqrt(1/9*1/5)=sqrt(1/9)*sqrt(1/5)=1/3sqrt(1/5)`

`sqrt(20)+sqrt(125)=sqrt(4*5)+sqrt(25*5)=sqrt(4)*sqrt(5)+sqrt(25)*sqrt(5)=2sqrt(5)+5sqrt(5)=7sqrt(5)`

`b) \ \ \  root(3)(24)=root(3)(8*3)=root(3)(8)*root(3)(3)=2*root(3)(3)`

`root(3)(32)=root(3)(8*4)=root(3)(8)*root(3)(4)=2root(3)(4)`

`root(3)(-48)=root(3)(-8*6)=root(3)(-8)*root(3)(6)=-2root(3)(6)`

`root(3)(1/81)=root(3)(1/27*1/3)=root(3)(1/27)*root(3)(1/3)=1/3root(3)(1/3)`

`root(3)(-108)=root(3)(-27*4)=root(3)(-27)*root(3)4=-3root(3)4`

`root(3)(135)-root(3)(-54)=root(3)(27*5)-root(3)(-27*2)=root(3)(27)*root(3)(5)-root(3)(-27)*root(3)(2)=`

`=3root(3)(5)-(-3root(3)(2))=3root(3)(5)+3root(3)(2)=3(root(3)(5)+root(3)(2))`

`c) \ \ \  sqrt(25x^2)=sqrt((5x)^2)=5x`

`sqrt(4x^6y^10)=sqrt(2^2*(x^3)^2*(y^5)^2)=2x^3y^5`

`root(3)(-27x^3y)=root(3)((-3x)^3*y)=-3xroot(3)(y)`

`root(3)(1/125x^9y^6z^12)=root(3)((1/5)^3(x^3)^3(y^2)^3(z^4)^3)=1/5x^3y^2z^4`