Odpowiedź:
9.
√(1 7/9) * 3³ - (1/4)² = √(16/9) * 27 - 1/16 = 4/3 * 27 - 1/16 = 4 * 9 - 1/16 =
= 36 - 1/16 = 35 16/16 - 1/16 = 35 15/16
10.
a) 3√5 * √7 = 3√(5 * 7) = 3√35
b) 15√10/3√5 = 15/3 * √(10/5) = 5 * √2 = 5√2
c) 5∛3 * ∛2 = 5∛(3 * 2) = 5∛6
d) 10∛12/2∛(- 4) = 10/2 * ∛(- 12/4) = 5 * ∛(- 3) = 5 * (- ∛3) = - 5∛3
11.
a) √28 = √(4 * 7) = √4 * √7 = 2√7
b) √3⁵ = √(3² * 3² * 3) = √3² * √3² * √3 = 3 * 3 * √3 = 9√3
c) ∛250 = ∛(125 * 2) = ∛125 * ∛2 = ∛5³ * ∛2 = 5 * ∛2 = 5∛2
d) ∛5⁵ = ∛(5³ * 5²) = ∛5³ * ∛5² = 5 * ∛5² = 5∛5² = 5∛25
12.
a - jeden bok = 2√6 [j]
[j] - znaczy właściwa jednostka
b - drugi bok = 3√2 [j]
P - pole = a * b = 2√6 * 3√2 = 2 * 3 * √(6 * 2) = 6√12 = 6√(4 * 3) =
= 6 * 2√3 = 12√3 [j]²
13.
a) ∛1000 + √16 = ∛10³+ √4² = 10+ 4 = 144
b) ∛(5² + 10²) = ∛(25 + 100) = ∛125 = ∛5³ = 5
c) √5²+ ∛17³= 5 + 17 = 22
d) (√73 + √2)/√2 = [√(36 * 2) + √2]/√2 = (6√2 + √2)/√2 = 7√2/√2 = 7
e) ∛2 * ∛32 + √2 * √8 = ∛(2 * 32) + √(2 * 8) = ∛64 + √16 =
= ∛4³ + √4² = 4 + 4 = 8
