Odpowiedź:
zad 1
√16 = √4² = 4 √121 = √11² = 11 - 5² = - 25
∛64 = ∛4³ = 4 ∛27 = ∛3³ = 3 (1 1/2)³ = (3/2)³ = 27/8 = 3 3/8
zad 2
12⁴ : 4⁴ = (12/4)⁴ = 3⁴ = 81
- 4²/√(25 - 9) = - 16/√16 = - 16/4 = - 4
27⁵ : (3⁴ * 9²)² = (3³)⁵ : [(3⁴ * (3²)²]² = 3¹⁵ : (3⁴ * 3⁴)² = 3¹⁵ : (3⁸)² =
= 3¹⁵ : 3¹⁶ = 3¹⁵⁻¹⁶ = 3⁻¹ = 1/3
√8,1 * √10 = √(8,1 * 10) = √81 = √9² = 9
0,5² * 14² = (0,5 * 14)² = 7² = 49
(√5)⁶ = (√5)² * (√5)² * (√5)² = 5 * 5 * 5 = 125
0,32³ : 0,08³ = (0,32/0,08)³ = 4³ = 64
(∛- 18)³ = - ∛18³ = - 18
(6⁴ * 6²)/(6⁷ : 6³) = 6⁴⁺²/6⁷⁻³ = 6⁶/6⁴ = 6⁶⁻⁴ = 6² = 36
∛540/∛20 = ∛(540/20) = ∛27 = ∛3³ = 3
√50 + √18 = √(25 * 2) + √(9 * 2) = 5√2 + 3√2) = 8√2
√2 * √8 - √(9 * 25) - ∛(54 : 2) + (√3)² - ∛(1000 : 125) =
= √(2 * 8) - √225 - ∛27 + 3 - ∛8 = √16 - 15 - 3 + 3 - 2 = 4 - 17 = - 13
zad 3
a - dłuższa podstawa = √32 = √(16 * 2) = 4√2 [j]
b - krótsza podstawa = 2√2 [j]
h - wysokość trapezu = 2 [j]
c - ramię trapezu = 2√3 [j]
o - obwód trapezu = a + b + h + c = 4√2 + 2√2 + 2 + 2√3 =
= 6√2 + 2 + 2√3 = 2(3√2 + 1 + √3) [j]
P - pole trapezu = 1/2 * (a + b) * h = 1/2 * (4√2 + 2√2) * 2 =
= 1/2 * 6√2 * 2 = 3√2 * 2 = 6√2 [j²]
[j] - znaczy właściwa jednostka