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DZIAŁANIA NA 
PIERWIASTKACH 
WYŁĄCZANIE CZYNNIKA PRZED ZNAK PIERWIASTKA 
Opracowała: mgr Joanna Stróżyk
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 
• 256 = 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
To już jasne, bo 22 = 4 
• 4 = 2 
• 256 = 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 4 ⋅ 64 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
Korzystamy ze wzoru: 
• 4 = 2 
푎 ⋅ 푏 = 푎 ⋅ 푏 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 
• 8 = 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 
• 8 = 
• 768 = 
Ponieważ 22 = 4 oraz 82 = 64.
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 
• 8 = 4 ⋅ 2 = 4 ⋅ 2 
• 768 =
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• ퟒ = ퟐ 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 
• 8 = 4 ⋅ 2 = ퟒ ⋅ 2 = ퟐ 2 
• 768 = 
Ponieważ 22 = 4, ale nie 2 nie 
jest liczbą wymierną, więc 
zostawiamy.
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 
• 8 = 4 ⋅ 2 = 4 ⋅ 2 = 2 2 
• 768 = 256 ⋅ 3 = 256 ⋅ 3 
Korzystamy ze wzoru: 
푎 ⋅ 푏 = 푎 ⋅ 푏
JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? 
Oblicz: 
• 4 = 2 
• ퟐퟓퟔ = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = ퟏퟔ 
• 8 = 4 ⋅ 2 = 4 ⋅ 2 = 2 2 
• 768 = 256 ⋅ 3 = ퟐퟓퟔ ⋅ 3 = ퟏퟔ 3 
Ponieważ 162 = 256, ale nie 3 
nie jest liczbą wymierną, więc 
zostawiamy.
POWODZENIA! 
WYŁĄCZANIE CZYNNIKA PRZED ZNAK PIERWIASTKA 
Opracowała: mgr Joanna Stróżyk

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Działania na pierwiastkach1

  • 1. DZIAŁANIA NA PIERWIASTKACH WYŁĄCZANIE CZYNNIKA PRZED ZNAK PIERWIASTKA Opracowała: mgr Joanna Stróżyk
  • 2. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = • 256 = • 8 = • 768 =
  • 3. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = • 8 = • 768 =
  • 4. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: To już jasne, bo 22 = 4 • 4 = 2 • 256 = • 8 = • 768 =
  • 5. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = 4 ⋅ 64 • 8 = • 768 =
  • 6. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = 4 ⋅ 64 = 4 ⋅ 64 • 8 = • 768 =
  • 7. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: Korzystamy ze wzoru: • 4 = 2 푎 ⋅ 푏 = 푎 ⋅ 푏 • 256 = 4 ⋅ 64 = 4 ⋅ 64 • 8 = • 768 =
  • 8. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 • 8 = • 768 = Ponieważ 22 = 4 oraz 82 = 64.
  • 9. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 • 8 = 4 ⋅ 2 = 4 ⋅ 2 • 768 =
  • 10. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • ퟒ = ퟐ • 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 • 8 = 4 ⋅ 2 = ퟒ ⋅ 2 = ퟐ 2 • 768 = Ponieważ 22 = 4, ale nie 2 nie jest liczbą wymierną, więc zostawiamy.
  • 11. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • 256 = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = 16 • 8 = 4 ⋅ 2 = 4 ⋅ 2 = 2 2 • 768 = 256 ⋅ 3 = 256 ⋅ 3 Korzystamy ze wzoru: 푎 ⋅ 푏 = 푎 ⋅ 푏
  • 12. JAK WYŁĄCZYĆ CZYNNIK PRZED ZNAK PIERWIASTKA? Oblicz: • 4 = 2 • ퟐퟓퟔ = 4 ⋅ 64 = 4 ⋅ 64 = 2 ⋅ 8 = ퟏퟔ • 8 = 4 ⋅ 2 = 4 ⋅ 2 = 2 2 • 768 = 256 ⋅ 3 = ퟐퟓퟔ ⋅ 3 = ퟏퟔ 3 Ponieważ 162 = 256, ale nie 3 nie jest liczbą wymierną, więc zostawiamy.
  • 13. POWODZENIA! WYŁĄCZANIE CZYNNIKA PRZED ZNAK PIERWIASTKA Opracowała: mgr Joanna Stróżyk