Question

Matematyka, załącznik

Zadanie 15. Rozłóż liczbę na czynniki pierwsze i wyłącz czynnik przed znak pierwiastka 3√432

Answer 1

Zad 11. 
3/4 ^ (-1) + 1/3 ^(-2) = 4/3 + 3/1^2 = 4/3 + 9 = 10 i 1/3
Zad 12.
1/√2 = 1/√2 * √2/√2 = √2/(√2)² = √2/2
Zad 13. 
2x√3=6 |:2
x√3 =3 |*√3
3x=3√3
x = √3
Zad 14. 
√(3*3*4*4*5*5) = √3²*4²*5²=3*4*5 = 60
Zad 15. 3√432 = 3√2*216 = 3√2*2*108 = 3√2*2*2*54= 3√2*2*2*2*27=3√2*2*2*2*3*9=3√2²*2²*3*3²=3*2*2*3√3=36√3
Zad 16. 
(∛2) ^ 9 = (2^1/3)^9 = 2 ^(1/3*9) = 2^3 = 8
Zad 17.
√7*5√7 = 5*√7*7 = 5*√7² = 5*7 = 35
Zad 18. 
(3 - 2√3) / 4√3 = (3 - 2√3) / 4√3 * √3/√3 = (3√3 - 2*3) / 4*3 = (√3 - 2) / 4
Zad 19. 
(7√2 - 3√8)*√2 = 7*2 - 3√8*2 = 14 - 3√16= 14 - 3*4 = 14-12=2
Zad 20. 
3* (1/2)^-2 - 4*(1/3)*-1 = 3 * (2/1)^2 - 4*(3/1)^1 = 0 = 3*4 - 4*3 = 0
Zad 21.
3^-2 - 2^-2 +6² = 1/3² - 1/2² + 36  = 1/9 - 1/4 + 36 = 4/36 - 9/36 + 36 = 36 - 5/36 = 35 i 31/36
Zad 22. 
4∛b² = 2²∛b² = ∛(2²)³b² = ∛64b²
Zad 23.
∛40 = ∛8*5=2∛5
Zad 24.
∛25 : ∛1/5 = ∛25 : 1/∛5 = ∛25 * ∛5 = ∛125 = ∛5³ = 5
Zad 25. 
∛24 = ∛8*3 = 2∛3
Zad 26.
10^-1 = 1/10^1 = 1/10 = 0,1
Zad 27.
(2/3)^-2 : (1/4)² = 1/(2/3)² : 1/16 = 1/4/9 * 16 = 9/4 * 16 = 9*4 = 36
Zad 28.
3/2√5 = 3/2√5 *√5/√5 = 3√5/2√5² = 3√5/2*5=3√5/10=0,3√5