Odpowiedź:
zad 1
a)
√8² + (√7)² - √2² = 8 + 7 - 2 = 13
b)
2√7² - 3√8² + 2∛8 = 2 * 7 - 3 * 8 + 2 * 2 = 14 - 24 + 4 = - 6
c)
√7² + √6 - (√6)² = 7 + √6 - 6 = 1 + √6
d)
∛12³ - (√17)² - √5 = 12 - 17 - √5 = - 2 - √5
e)
3√5² + 2√5 - 2∛5³ = 3 * 5 + 2√5 - 2 * 5 = 15 + 2√5 - 10 =
= 5 + 2√5
zad 2
√36 * √4 = 12 2√144 - ∛1 = 23
∛1000 : √25 = 2 2 * √2 1/4 + 2 * √16 = 11
zad 3
(- 1 1/2)⁷ * (- 1 1/2) : (- 1 1/2)⁶ = (- 1 1/2)⁷⁺¹⁻⁶ = (- 1 1/2)² = (3/2)² = 9/4 = 2 1/4 --- T
[(- 0,2)³ * (- 0,2)⁴ * (- 0,2)⁵]/[(- 0,2)⁸ * (- 0,2)⁴] = (- 0,2)³⁺⁴⁺⁵/(- 0,2)⁸⁺⁴ =
= (- 0,2)¹²/(- 0,2)¹² = 1 ---- I
[(1/4)⁸ * 8⁴]/[(1/4)⁷ * 8³] = (4⁻⁸ * 8⁴)/(4⁻⁷ * 8³) = [(2²)⁻⁸ * (2³)⁴]/[(2²)⁻⁷ * (2³)³] =
= (2⁻¹⁶ * 2¹²)/(2⁻¹⁴ * 2⁹) = 2⁻¹⁶⁺¹²/2⁻¹⁴⁺⁹ = 2⁻⁴/2⁻⁵ = 2⁻⁴⁺⁵ = 2¹ = 2 ---- L
[5⁸ * (0,1)⁷]/[5⁶ * (0,1)⁴] = 5⁸⁻⁶ * (0,1)⁷⁻⁴ = 5² * (0,1)³ = 25 * 0,001 = 0,025 =
= 25/1000 = 1/40 ---- E
[(- 0,1)⁷ * (- 0,1)²]/[(0,1)⁵ * (0,1)⁴] = (- 0,1)⁷⁺²/(0,1)⁵⁺⁴ = (- 0,1)⁹/(0,1)⁹ = - 1 ------- 0
(- 1 1/2)⁵ * (- 1 1/2)⁸ : (1 1/2)¹¹
(- 1 1/2)⁵⁺⁸ : (1 1/2)¹¹ = (- 1 1/2)¹³ : (1 1/2)¹¹ = - (1 1/2)¹³⁻¹¹ = - (1 1/2)² = - (3/2)² =
= - 9/4 = - 2 1/4 ----- W
- 2 1/4 1 2 1/4 1/40 2 - 1
W I T E L O
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Odpowiedź:
zad 1
a)
√8² + (√7)² - √2² = 8 + 7 - 2 = 13
b)
2√7² - 3√8² + 2∛8 = 2 * 7 - 3 * 8 + 2 * 2 = 14 - 24 + 4 = - 6
c)
√7² + √6 - (√6)² = 7 + √6 - 6 = 1 + √6
d)
∛12³ - (√17)² - √5 = 12 - 17 - √5 = - 2 - √5
e)
3√5² + 2√5 - 2∛5³ = 3 * 5 + 2√5 - 2 * 5 = 15 + 2√5 - 10 =
= 5 + 2√5
zad 2
√36 * √4 = 12 2√144 - ∛1 = 23
∛1000 : √25 = 2 2 * √2 1/4 + 2 * √16 = 11
zad 3
(- 1 1/2)⁷ * (- 1 1/2) : (- 1 1/2)⁶ = (- 1 1/2)⁷⁺¹⁻⁶ = (- 1 1/2)² = (3/2)² = 9/4 = 2 1/4 --- T
[(- 0,2)³ * (- 0,2)⁴ * (- 0,2)⁵]/[(- 0,2)⁸ * (- 0,2)⁴] = (- 0,2)³⁺⁴⁺⁵/(- 0,2)⁸⁺⁴ =
= (- 0,2)¹²/(- 0,2)¹² = 1 ---- I
[(1/4)⁸ * 8⁴]/[(1/4)⁷ * 8³] = (4⁻⁸ * 8⁴)/(4⁻⁷ * 8³) = [(2²)⁻⁸ * (2³)⁴]/[(2²)⁻⁷ * (2³)³] =
= (2⁻¹⁶ * 2¹²)/(2⁻¹⁴ * 2⁹) = 2⁻¹⁶⁺¹²/2⁻¹⁴⁺⁹ = 2⁻⁴/2⁻⁵ = 2⁻⁴⁺⁵ = 2¹ = 2 ---- L
[5⁸ * (0,1)⁷]/[5⁶ * (0,1)⁴] = 5⁸⁻⁶ * (0,1)⁷⁻⁴ = 5² * (0,1)³ = 25 * 0,001 = 0,025 =
= 25/1000 = 1/40 ---- E
[(- 0,1)⁷ * (- 0,1)²]/[(0,1)⁵ * (0,1)⁴] = (- 0,1)⁷⁺²/(0,1)⁵⁺⁴ = (- 0,1)⁹/(0,1)⁹ = - 1 ------- 0
(- 1 1/2)⁵ * (- 1 1/2)⁸ : (1 1/2)¹¹
(- 1 1/2)⁵⁺⁸ : (1 1/2)¹¹ = (- 1 1/2)¹³ : (1 1/2)¹¹ = - (1 1/2)¹³⁻¹¹ = - (1 1/2)² = - (3/2)² =
= - 9/4 = - 2 1/4 ----- W
- 2 1/4 1 2 1/4 1/40 2 - 1
W I T E L O