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 simplify the expression, we need to simplify each square root term by factoring out perfect squares. Step 1: Simplify each term. 5sqrt(243) = 5sqrt(81 × 3) = 5 × 9sqrt(3) = 45sqrt(3) 2sqrt(27) = 2sqrt(9 × 3) = 2 × 3sqrt(3) = 6sqrt(3) sqrt(75) = sqrt(25 × 3) = 5sqrt(3) 3sqrt(48) = 3sqrt(16 × 3) = 3 × 4sqrt(3) = 12sqrt(3) Step 2: Substitute the simplified terms back into the original expression. 45sqrt(3) + 6sqrt(3) - 5sqrt(3) - 12sqrt(3) Step 3: Combine the coefficients of sqrt(3). (45 + 6 - 5 - 12)sqrt(3) (51 - 5 - 12)sqrt(3) (46 - 12)sqrt(3) 34sqrt(3) The simplified form is 34sqrt(3). Comparing this with the given options, it matches option A. The final answer is A. 34sqrt(3). Send me the next one 📸