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
Here are the solutions for the problems: 3. (c) 169000 is perfect square number. To determine if a number is a perfect square, we check its prime factorization. If all the exponents in the prime factorization are even, then the number is a perfect square. Step 1: Find the prime factorization of 169000. 169000 = 169 × 1000 169 = 13 × 13 = 13^2 1000 = 10 × 10 × 10 = (2 × 5) × (2 × 5) × (2 × 5) = 2^3 × 5^3 So, 169000 = 13^2 × 2^3 × 5^3 Step 2: Check the exponents. The exponents of the prime factors are 2 (for 13), 3 (for 2), and 3 (for 5). Since the exponents 3 are odd, 169000 is not a perfect square. ❌ Incorrect. 169000 is not a perfect square number. 4. Find the square root of the following using the factorization method: a) 169 Step 1: Find the prime factorization of 169. 169 = 13 × 13 = 13^2 Step 2: Find the square root. sqrt(169) = sqrt(13^2) = 13 b) 324 Step 1: Find the prime factorization of 324. 324 = 2 × 162 162 = 2 × 81 81 = 3 × 27 27 = 3 × 9 9 = 3 × 3 So, 324 = 2 × 2 × 3 × 3 × 3 × 3 = 2^2 × 3^4 Step 2: Find the square root. sqrt(324) = sqrt(2^2 × 3^4) = 2^(2)/(2) × 3^(4)/(2) = 2^1 × 3^2 = 2 × 9 = 18 c) 1225 Step 1: Find the prime factorization of 1225. 1225 = 5 × 245 245 = 5 × 49 49 = 7 × 7 So, 1225 = 5 × 5 × 7 × 7 = 5^2 × 7^2 Step 2: Find the square root. sqrt(1225) = sqrt(5^2 × 7^2) = 5^(2)/(2) × 7^(2)/(2) = 5^1 × 7^1 = 5 × 7 = 35 Drop the next question! 📸