This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hapa kuna hatua za kutatua tatizo hili bila kutumia kikokotoo au jedwali: Step 1: Rahisisha nambari ya juu (numerator). Tunayo sqrt(45 × (2.04)^2). Tunajua kwamba sqrt(ab) = sqrt(a) × sqrt(b) na sqrt(x^2) = x. sqrt(45 × (2.04)^2) = sqrt(45) × sqrt((2.04)^2) = sqrt(9 × 5) × 2.04 = sqrt(9) × sqrt(5) × 2.04 = 3sqrt(5) × 2.04 Step 2: Rahisisha nambari ya chini (denominator). Tunayo 2.89 × sqrt(0.05). Tunajua kwamba 0.05 = (5)/(100). 2.89 × sqrt(0.05) = 2.89 × sqrt((5)/(100)) = 2.89 × sqrt(5)sqrt(100) = 2.89 × sqrt(5)10 Step 3: Badilisha sehemu zilizorahisishwa kwenye usemi wa asili. 3sqrt(5) × 2.042.89 × sqrt(5)10 Futa sqrt(5) kutoka juu na chini: (3 × 2.04)/(2.89 × 1)10 Step 4: Badilisha desimali kuwa sehemu ili kurahisisha mgawanyiko. Tunajua 2.04 = (204)/(100) na 2.89 = (289)/(100). (3 × 204)/(100)(289)/(100) × (1)/(10) (3 × 204)/(100)(289)/(1000) Geuza mgawanyiko kuwa kuzidisha kwa kugeuza sehemu ya chini: (3 × 204)/(100) × (1000)/(289) Futa 100: (3 × 204 × 10)/(289) Step 5: Fanya hesabu ya mwisho. Tunajua 289 = 17^2 na 204 = 17 × 12. (3 × (17 × 12) × 10)/(17 × 17) Futa 17 moja kutoka juu na chini: (3 × 12 × 10)/(17) (36 × 10)/(17) (360)/(17) Kama nambari mchanganyiko, hii ni 21 (3)/(17). Jibu la mwisho ni: (360)/(17) Tuma swali linalofuata 📸