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.
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आपको अभाज्य गुणनखंडन (prime factorization) विधि का उपयोग करके संख्याओं का वर्गमूल ज्ञात करना है। a) 81 Step 1: 81 के अभाज्य गुणनखंड ज्ञात करें। 81 = 3 × 27 27 = 3 × 9 9 = 3 × 3 इसलिए, 81 = 3 × 3 × 3 × 3 = 3^4 Step 2: वर्गमूल ज्ञात करें। sqrt(81) = sqrt(3 × 3 × 3 × 3) = sqrt((3 × 3) × (3 × 3)) = sqrt(9 × 9) = sqrt(9^2) = 9 sqrt(81) = 9 b) 625 Step 1: 625 के अभाज्य गुणनखंड ज्ञात करें। 625 = 5 × 125 125 = 5 × 25 25 = 5 × 5 इसलिए, 625 = 5 × 5 × 5 × 5 = 5^4 Step 2: वर्गमूल ज्ञात करें। sqrt(625) = sqrt(5 × 5 × 5 × 5) = sqrt((5 × 5) × (5 × 5)) = sqrt(25 × 25) = sqrt(25^2) = 25 sqrt(625) = 25 c) 1024 Step 1: 1024 के अभाज्य गुणनखंड ज्ञात करें। 1024 = 2 × 512 512 = 2 × 256 256 = 2 × 128 128 = 2 × 64 64 = 2 × 32 32 = 2 × 16 16 = 2 × 8 8 = 2 × 4 4 = 2 × 2 इसलिए, 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^10 Step 2: वर्गमूल ज्ञात करें। sqrt(1024) = sqrt(2^10) = 2^(10)/(2) = 2^5 2^5 = 2 × 2 × 2 × 2 × 2 = 32 sqrt(1024) = 32 अगला प्रश्न भेजो 📸