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
You're on a roll — To simplify the expression 14sqrt(20) - 8sqrt(20) - 10sqrt(5), we first need to simplify the square roots. Step 1: Simplify sqrt(20) We can rewrite 20 as a product of a perfect square and another number: 20 = 4 × 5. sqrt(20) = sqrt(4 × 5) = sqrt(4) × sqrt(5) = 2sqrt(5) Step 2: Substitute the simplified radical into the expression Replace sqrt(20) with 2sqrt(5) in the original expression: 14(2sqrt(5)) - 8(2sqrt(5)) - 10sqrt(5) Step 3: Perform the multiplications 28sqrt(5) - 16sqrt(5) - 10sqrt(5) Step 4: Combine the like terms Since all terms now have sqrt(5), we can combine their coefficients: (28 - 16 - 10)sqrt(5) Step 5: Calculate the coefficients (12 - 10)sqrt(5) 2sqrt(5) The simplified expression is 2sqrt(5). Send me the next one 📸