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, we will simplify each radical term and then combine like terms. The expression is: sqrt(150) - 3sqrt(3)(2sqrt(2) - 5) - 5sqrt(32) Step 1: Simplify each square root. sqrt(150) = sqrt(25 × 6) = sqrt(25) × sqrt(6) = 5sqrt(6) sqrt(32) = sqrt(16 × 2) = sqrt(16) × sqrt(2) = 4sqrt(2) Step 2: Distribute the term 3sqrt(3) into the parentheses (2sqrt(2) - 5). 3sqrt(3)(2sqrt(2) - 5) = (3sqrt(3) × 2sqrt(2)) - (3sqrt(3) × 5) = (3 × 2 × sqrt(3 × 2)) - (3 × 5 × sqrt(3)) = 6sqrt(6) - 15sqrt(3) Step 3: Substitute the simplified terms back into the original expression. 5sqrt(6) - (6sqrt(6) - 15sqrt(3)) - 5(4sqrt(2)) Step 4: Remove the parentheses and simplify the last term. 5sqrt(6) - 6sqrt(6) + 15sqrt(3) - 20sqrt(2) Step 5: Combine like terms. (5sqrt(6) - 6sqrt(6)) + 15sqrt(3) - 20sqrt(2) -sqrt(6) + 15sqrt(3) - 20sqrt(2) The terms are all unlike, so they cannot be combined further. The final answer is -sqrt(6) + 15sqrt(3) - 20sqrt(2). That's 2 down. 3 left today — send the next one.