Matematyka

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

Wydawnictwo:WSiP

Rok wydania:2016

Wykonaj działania. (4√0,72-3√4,5+4,6√2)/(-5√1,5+0,3√6-2√0,96) 4.6 gwiazdek na podstawie 5 opinii
  1. Gimnazjum
  2. 2 Klasa
  3. Matematyka

Wykonaj działania. (4√0,72-3√4,5+4,6√2)/(-5√1,5+0,3√6-2√0,96)

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a)

Upraszczamy najpierw licznik i mianownik ułamka.

Licznik:

`4sqrt(0,72)-3sqrt(4,5)+4,6sqrt(2)=4sqrt(0,36*2)-3sqrt(9*0,5)+4,6sqrt(2)=4sqrt(0,36)*sqrt(2)-3sqrt(9)*sqrt(0,5)+4,6sqrt(2)=4*0,6*sqrt(2)-3*3sqrt(0,5)+4,6sqrt(2)=`

`=2,4sqrt(2)-9sqrt(0,5)+4,6sqrt(2)=7sqrt(2)-9sqrt(0,5)` 

 

Mianownik:

`-5sqrt(1,5)+0,3sqrt(6)-2sqrt(0,96)=-5sqrt(1,5)+0,3sqrt(4*1,5)-2sqrt(0,64*1,5)=-5sqrt(1,5)+0,3sqrt(4)*sqrt(1,5)-2sqrt(0,64)*sqrt(1,5)=`

`-5sqrt(1,5)+0,3*2sqrt(1,5)-2*0,8sqrt(1,5)=-5sqrt(1,5)+0,6sqrt(1,5)-1,6sqrt(1,5)=-6sqrt(1,5)`

Wstawiamy wyniki do ułamka:

`(4sqrt(0,72)-3sqrt(4,5)+4,6sqrt(2))/(-5sqrt(1,5)+0,3sqrt(6)-2sqrt(0,96))=(7sqrt(2)-9sqrt(0,5))/(-6sqrt(1,5))=(7sqrt(2)-9sqrt(0,5)):(-6sqrt(1,5))=7sqrt(2):(-6sqrt(1,5))-9sqrt(0,5):(-6sqrt(1,5))=`

`=-7/6sqrt(2/(1,5))+9/6sqrt((0,5)/(1,5))=-7/6sqrt(20/15)+9/6sqrt(5/15)=-7/6sqrt(4/3)+9/6sqrt(1/3)=-7/6sqrt(4*1/3)+9/6sqrt(1/3)=-7/6*sqrt(4)*sqrt(1/3)+9/6sqrt(1/3)=`

`=-7/6*2sqrt(1/3)+9/6sqrt(1/3)=-14/6sqrt(1/3)+9/6sqrt(1/3)=-5/6sqrt(1/3)=-5/6*(sqrt(1)/sqrt(3))=-5/6*1/sqrt(3)=-5/6*sqrt(3)/3=-5/18*sqrt(3)`

b)

Analogicznie do poprzedniego przykładu- wykonujemy działanie stopniowe.

`-10root(3)(0,192)-1 4/5root(3)(3)+5,6root(3)(3/8)=-10root(3)(0,064*3)-9/5root(3)(3)+56/10root(3)(1/8*3)=-10root(3)(0,064)*root(3)(3)-9/5root(3)(3)+56/10root(3)(1/8)*root(3)(3)=`

`=-10*0,4*root(3)(3)-9/5root(3)(3)+56/10*1/2*root(3)(3)=-4root(3)(3)-9/5root(3)(3)+14/5root(3)(3)=-4root(3)(3)+5/5root(3)(3)=-4root(3)(3)+root(3)(3)=-3root(3)(3)`

`5root(3)(0,054)-4,5root(3)(2/125)=5root(3)(0,027*2)-4,5root(3)(1/125*2)=5root(3)(0,027)*root(3)(2)-4,5root(3)(1/125)*root(3)(2)=5*0,3*root(3)(2)-4,5*1/5*root(3)(2)=`

`=1,5*root(3)(2)-4,5*0,2*root(3)(2)=1,5root(3)(2)-0,9root(3)(2)=0,6root(3)(2)`

`(-10root(3)(0,192)-1 4/5root(3)(3)+5,6root(3)(3/8))/(5root(3)(0,054)-4,5root(3)(2/125))=(-3root(3)(3))/(0,6root(3)(2))=-3/(0,6)*(root(3)(3)/root(3)(2))=-3/(0,6)*(root(3)(3)*root(3)(2^2))/(root(3)(2)*root(3)(2^2))=`

`=-30/6*(root(3)(3)*root(3)(2)*root(3)(2))/(root(3)(2))^3=-5*root(3)(3*2*2)/2=-5/2*root(3)(12)`

c)

`8sqrt(2,45)+1,2sqrt(5/9)-2,25sqrt(3 77/81)=8sqrt(0,49*5)+1,2sqrt(1/9*5)-2,25sqrt(320/81)=8sqrt(0,49)*sqrt(5)+1,2sqrt(1/9)*sqrt(5)-2 25/100sqrt(64/81*5)=`

`=8*0,7*sqrt(5)+1,2*1/3*sqrt(5)-2 1/4*sqrt(64/81)*sqrt(5)=5,6sqrt(5)+12/10*1/3sqrt(5)-9/4*8/9sqrt(5)=5,6sqrt(5)+4/10sqrt(5)-8/4sqrt(5)=`

`=5,6sqrt(5)+0,4sqrt(5)-2sqrt(5)=4sqrt(5)`

`5sqrt(3,63)+17 1/2sqrt(3/49)=5sqrt(1,21*3)+ 35/2sqrt(1/49*3)=5sqrt(1,21)*sqrt(3)+35/2sqrt(1/49)*sqrt(3)=5*1,1sqrt(3)+35/2*1/7sqrt(3)=`

`5,5sqrt(3)+5/2sqrt(3)=5,5sqrt(3)+2 1/2sqrt(3)=5,5sqrt(3)+2,5sqrt(3)=8sqrt(3)`

`(8sqrt(2,45)+1,2sqrt(5/9)-2,25sqrt(3 77/81))/(5sqrt(3,63)+17 1/2sqrt(3/49))=(4sqrt(5))/(8sqrt(3))=4/8*sqrt(5)/sqrt(3)=1/2*(sqrt(5)*sqrt(3))/3=1/6sqrt(5*3)=1/6sqrt(15)=sqrt(15)/6`