Zad.1 a) √16/49 = √16/√49 = 4/7 √25/81 = √25/√81 = 5/9 √121/64 = √121/√64 = 11/8 = 1 3/8 √400/169 = √400/√169 = 20/13 = 1 7/13 b) √2 1/4 = √9/4 = √9/√4 = 3/2 = 1,5 √1 9/16 = √25/16 = √25/√16 = 5/4 = 1,25 √11 1/9 = √100/9 = √100/√9 = 10/3 = 3 1/3 √2 14/25 = √64/25 = √64/√25 = 8/5 = 1,6 Zad.2 a) √18 = √9×√2 = 3√2 b) √50 = √25×√2 = 5√2 c) √48 = √16×√3 = 4√3 d) √108 = √36×√3 = 6√3 e) √450 = √225×√2 = 15√2 Zad.3 a) 4√2+√8 = 4√2+√4×√2 = 4√2+2√2 = 6√2 b) √32-3√2 = √16×√2-3√2 = 4√2-3√2 = √2 c) √18+√8 = √9×√2+√4×√2 = 3√2+2√2 = 5√2 d) √200-√50 = √100×√2-√25×√2 = 10√2-5√2 = 5√2 e) √18+√72+√98 = √9×√2+√36×√2+√49×√2 = 3√2+6√2+7√2 = 16√2 Zad.4 a) 7√5+√20 = 7√5+√4×√5 = 7√5+2√5 = 9√5 b) √48-√3 = √16×√3-√3 = 4√3-√3 = 3√3 c) √12+√27 = √4×√3+√9×√3 = 2√3+3√3 = 5√3 d) √45-√125 = √9×√5-√25×√5 = 3√5-5√5 = -2√5 Zad.5 a) 3√2 = √3²×√2 = √9×√2 = √18 b) 2√3 = √2²×√3 = √4×√3 = √12 c) 2√6 = √2²×√6 = √4×√6 = √24 d) 3√7 = √3²×√7 = √9×√7 = √63 e) 7√3 = √7²×√3 = √49×√3 = √147 Zad.6 a) √12×√3 = √36 = 6 b) √32×√8 = √256 = 16 c) √10×√40 = √400 = 20 d) √18×√50 = √900 = 30 e) √28×√63 = √1764 = 42 f) √45×√20 = √900 = 30 g) √30×√480 = √14400 = 120 h) √80×√180 = √14400 = 120 Zad.7 a)∛8/125 = ∛8/∛125 = 2/5 = 0,4 ∛27/8000 = ∛27/∛8000 = 3/20 = 0,15 ∛2 10/27 = ∛64/27 = ∛64/∛27 = 4/3 = 1 1/3 ∛1 61/64 = ∛125/64 = ∛125/∛64 = 5/4 = 1,25 b) ∛2×∛4 = ∛8 = 2 ∛50×∛20 = ∛1000 = 10 ∛36×∛6 = ∛216 = 6 Zad.8 a) ∛32 = ∛8×∛4 = 2∛4 b) ∛250 = ∛125×∛2 = 5∛2 c) ∛135 = ∛27×∛5 = 3∛5 d) ∛375 = ∛125×∛3 = 5∛3 e) ∛108 = ∛64×∛2 = 4∛2 Zad.9 a) 2∛3 = ∛2³×∛3 = ∛8×∛3 = ∛24 b) 3∛2 = ∛3³×∛2 = ∛27×∛2 = ∛54 c) 5∛2 = ∛5³×∛2 = ∛125×∛2 = ∛250 d) 2¹⁰√3 = ¹⁰√2¹⁰×¹⁰√3 = ¹⁰√1024×¹⁰√3 = ¹⁰√3072 e) 6∛5 = ∛6³×∛5 = ∛216×∛5 = ∛1080 Nie zrobiłem parę przykładów, bo są za trudne. POZDRAWIAM :)
