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 each part: a) sqrt(64 × 36) Method 1: Calculate the product first, then take the square root. sqrt(64 × 36) = sqrt(2304) = 48 Method 2: Take the square root of each number, then multiply. sqrt(64) × sqrt(36) = 8 × 6 = 48 The statements give the same answer. This is because sqrt(a × b) = sqrt(a) × sqrt(b). b) sqrt(169 - 25) Method 1: Calculate the difference first, then take the square root. sqrt(169 - 25) = sqrt(144) = 12 Method 2: Take the square root of each number, then subtract. sqrt(169) - sqrt(25) = 13 - 5 = 8 The statements give different answers. This is because sqrt(a - b) ≠ sqrt(a) - sqrt(b). c) sqrt(64 ÷ 16) Method 1: Calculate the division first, then take the square root. sqrt(64 ÷ 16) = sqrt(4) = 2 Method 2: Take the square root of each number, then divide. sqrt(64) ÷ sqrt(16) = 8 ÷ 4 = 2 The statements give the same answer. This is because sqrt(a ÷ b) = sqrt(a) ÷ sqrt(b). That's 2 down. 3 left today — send the next one.