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
To solve the expression sqrt(18) × sqrt(32), we can simplify each square root first. Step 1: Simplify sqrt(18). We find the largest perfect square factor of 18. 18 = 9 × 2 So, sqrt(18) = sqrt(9 × 2) = sqrt(9) × sqrt(2) = 3sqrt(2). Step 2: Simplify sqrt(32). We find the largest perfect square factor of 32. 32 = 16 × 2 So, sqrt(32) = sqrt(16 × 2) = sqrt(16) × sqrt(2) = 4sqrt(2). Step 3: Multiply the simplified square roots. sqrt(18) × sqrt(32) = (3sqrt(2)) × (4sqrt(2)) Multiply the coefficients and the square roots separately: = (3 × 4) × (sqrt(2) × sqrt(2)) \\ = 12 × (sqrt(2))^2 \\ = 12 × 2 \\ = 24 Alternatively, we can multiply the numbers inside the square root first: sqrt(18) × sqrt(32) = sqrt(18 × 32) \\ = sqrt(576) Now, find the square root of 576. sqrt(576) = 24 The final answer is 24.