Odpowiedź:
zad 1
a) √36 = √(6 * 6) = √6² = 6
b) √(25/81) = √(5/9 * 5/9) = √(5/9)² = 5/9
c) ∛(- 8/27) = - ∛(2/3 * 2/3 * 2/3) = - ∛(2/3)³ - 2/3
d) √0,64 = √(0,8 * 0,8) = √(0,8)² = 0,8
e) ∛(- 0,0001) = - √(0,1 * 0,1 * 0,1) = - ∛(0,1)³ = - 0,1
f) √121 = √(11 * 11) = √11² = 11
g) ∛64 = ∛(4 * 4 * 4) = ∛4³ = 4
h) ∛(2 10/27) = ∛(64/27) = ∛(4/3 * 4/3 * 4/3) = ∛(4/3)³ = 4/3 = 1 1/3
zad 2
(2 + √3)(1 + √3) = 2 + √3 + 2√3 + √3 * √3 = 2 + 3√3 + 3 = 5 + 3√3
(3 - √5)(√5 + 2) = 3√5 - √5 * √5 + 6 - 2√5 = √5 - 5 + 6 = √5 + 1
- √3(2√3 + 5) = - 2 * √3 * √3 - 5√3 = - 2 * 3 - 5√3 = - 6 - 5√3
zad 3
a) √7⁴ = √7² * √7² = 7 * 7 = 49
b) (4√5)² = 16 * 5 = 80
c) (3/2√6)² =3²/(4 * 6) = 9/24 = 3/8
d) (∛2)⁹ = (∛2³) * (∛2)³ * (∛2)³ = 2 * 2 * 2 = 8
e) (∛5)¹² = (∛5)³ * (∛5)³ * (∛5)³ * (∛5)³ = 5 * 5 * 5 * 5 = 625
f) (- 10∛(- 0,1)³ = (- 10)³ * [∛(- 0,1)]³ = - 1000 * (- 0,1) = 100
g) ∛(25√25) = ∛(25 * 5) = ∛(5 * 5 * 5) = ∛5³ = 5
h) (∛5)⁶ - (√2)⁶ = ∛5³ * ∛5³ - √2² * √2² * √2² = 5 * 5 - 2 * 2 * 2 = 25 - 8 = 7
zad 4
a) √44 = √(4 * 11) = √4 * √11 = √2² * √11 = 2√11
b) ∛40 = ∛(8 * 5) = ∛8 * ∛5 = ∛2³ * ∛5 = 2∛5
c) √12 + 5√3 = √(4 * 3) + 5√3 = √4 * √3 + 5√3 = √2² * √3 + 5√3 = 2√3 + 5√3 =
= 7√3
d) (√50 + √72)/√2 = [ √(25 * 2) + √(36 * 2)]/√2 = (5√2 + 6√2)/√2 = 11√2/√2 = 11
zad 5
a) 5√2 = √(5² * 2) = √(25 * 2) = √50
b) 2∛5 = ∛(2³ * 5) = ∛(8 * 5) = ∛40
c) 0,1√2000 = √(0,1² * 2000) = √(0,01 * 2000) = √20
d) 4∛(3/32) = ∛(4³ * 3/32) = ∛(64 * 3/32) = ∛(2 * 3) = ∛6
