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
Ili kurahisisha usemi huu, tunahitaji kuondoa mzizi wa mraba kutoka kwa denominator. Tunafanya hivyo kwa kuzidisha nambari na denominator kwa kiambishi cha denominator. Step 1: Zidisha nambari na denominator kwa kiambishi cha denominator. Kiambishi cha 7-3sqrt(5) ni 7+3sqrt(5). 3+sqrt(5)7-3sqrt(5) × 7+3sqrt(5)7+3sqrt(5) Step 2: Panua nambari. (3+sqrt(5))(7+3sqrt(5)) = 3(7) + 3(3sqrt(5)) + sqrt(5)(7) + sqrt(5)(3sqrt(5)) = 21 + 9sqrt(5) + 7sqrt(5) + 3(sqrt(5))^2 = 21 + 16sqrt(5) + 3(5) = 21 + 16sqrt(5) + 15 = 36 + 16sqrt(5) Step 3: Panua denominator. Tumia tofauti ya fomula ya mraba: (a-b)(a+b) = a^2 - b^2. (7-3sqrt(5))(7+3sqrt(5)) = 7^2 - (3sqrt(5))^2 = 49 - (3^2 × (sqrt(5))^2) = 49 - (9 × 5) = 49 - 45 = 4 Step 4: Unganisha nambari na denominator zilizorahisishwa. 36 + 16sqrt(5)4 Step 5: Rahisisha sehemu kwa kugawanya kila neno katika nambari kwa denominator. (36)/(4) + 16sqrt(5)4 9 + 4sqrt(5) Jibu la mwisho ni: 9 + 4sqrt(5) Tuma swali linalofuata 📸