Question

Pomocy!!!!~!!!

Temat:Pierwiastek z ilorzu, iloraz z pierwiastków....

zad1.

Rozwiąż równanie:

a)√20=x√5

b)∛40=x∛5

c)√20+√45=x√5

zad2

Oblicz

a) (3√50+2√8-√32):2=

b)(6√24-2√54+√96):√3=

c)(8∛-16+2∛-54-3∛-128):∛-2=

d)(4∛625-3∛40+∛320):∛5=

zad3

Oblicz:

a) (-6√0,54+15√0,06):√6=

b) (6∛40½-8∛12):2∛1,5=

Answer 1

zad1.

Rozwiąż równanie:

a)√20=x√5

  √(4*5) = x√5

  √4*√5 = x√5

   2√5 = x√5

    x = 2

 

b)∛40=x∛5

 ∛(8*5) = x∛5

 ∛8*∛5 = x∛5

    2∛5 = x∛5

     2 = x

     x =2

 

c)√20+√45=x√5

  √(4*5) + √(9*5) = x√5

  √4*√5 + √9*√5 = x√5

       2√5 +3√5 = x√5

             5√5 = x√5

            5 =x

            x =5

 

 

zad2

Oblicz

a) (3√50+2√8-√32):2=

=  [(3*√(25*2) +2*√(4*2) - √(16*2) ] :2 =

=  [ 3*√25*√2 +2*√4*√2 - √16*√2 ] : 2 =

= [ 3*5*√2 + 2*2*√2 - 4*√2 ] :2 =

= [ 15√2 +4√2 - 4√2 ] :2 =

= (15√2) :2 =

= (15/2)*√2 =

= 7,5*√2

 

b)(6√24-2√54+√96):√3=

= [ 6√(4*6) - 2*√(9*6) + √(16*6) ] : √3 =

= [ 6√4*√6 -2*√9*√6 + √16*√6  ] :√3 =

= [ 6*2*√6 - 2*3*√6 +4*√6 ] : √3 =

= [ 12√6 -6√6 + 4√6 ] : √3 =

= [  10√6 ] : √3 =

= 10*√(6:3) =

= 10*√2

 

c)(8∛-16+2∛-54-3∛-128):∛-2=

= [ 8∛(-8*2) + 2*∛(-27*2) - 3∛(-64*2) ] : ∛-2 =

= [ 8*∛8*∛-2 + 2*∛27*∛-2 - 3*∛64*∛-2 ] : ∛-2 =

= [ 8*2*∛-2 + 2*3*∛-2 - 3*4∛-2  ] : ∛-2 =

= [ 16∛-2 + 6∛-2 - 12∛-2 ] : ∛-2 =

= [ 10∛-2 ] : ∛-2 =

= 10

 

d)(4∛625-3∛40+∛320):∛5=

= [ 4*∛(125*5) - 3*∛(8*5) + ∛(64*5) ] : ∛5 =

= [ 4*∛125*∛5 - 3*∛8*∛5 + ∛64*∛5  ] : ∛5 =

= [ 4*5*∛5 - 3*2*∛5 + 4*∛5 ] : ∛5 =

= [ 20∛5 -6∛5 + 4∛5 ] : ∛5 =

= [ 18∛5 ] : ∛5 =

= 18

 

zad3

Oblicz:

a) (-6√0,54+15√0,06):√6=

 = [ 6*√(54/100) + 15*√ (6/100) ] : √6 =

= [ 6*√54 : √100 + 15*√6 : √100 ] : √6 =

= [ 6*√(9*6) : 10 + 15*√6 :10 ] :√6 =

= [ (6/10)*√9*√6  + (15/10)*√6 ] : √6 =

= [ 0,6*3*√6 + 1,5*√6 ] : √6 =

= [ 1,8*√6 + 1,5*√6 ] : √6 =

=  [ 3,3*√6 ] : √6 =

= 3,3

 

b) (6∛40½-8∛12):2∛1,5=

= [ 6*∛(81/2) -  8*∛(24/2)  ] : 2∛1,5 =

= [ (6*∛81) : ∛2 - 8*∛24:∛2 ] : 2∛1,5 =

= [ (6*∛27*∛2 ) : ∛3 - 8*∛(8*3) :∛2] : 2∛1,5 =

= [ 6*3*∛3 ):∛2     -  8*∛8 *∛3  : ∛2 ] : 2∛1,5 =

= [ 18*∛(3/2)  - 8*2* ∛(3/2) ] : 2∛1,5 =

= [ 18∛1,5 - 16∛1,5 ]  : 2∛1,5 =

= [  2∛1,5 ] : 2∛1,5 =

= 1