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 — Step 1: Solve 12sqrt(17) - 8sqrt(17). These are like surds, meaning they have the same radical part (sqrt(17)). To subtract them, subtract their coefficients. 12sqrt(17) - 8sqrt(17) = (12 - 8)sqrt(17) = 4sqrt(17) 4sqrt(17) Step 2: Solve 5sqrt(5) + sqrt(5). These are like surds. To add them, add their coefficients. Remember that sqrt(5) is equivalent to 1sqrt(5). 5sqrt(5) + 1sqrt(5) = (5 + 1)sqrt(5) = 6sqrt(5) 6sqrt(5) Step 3: Solve 5sqrt(7) × (2)/(5)sqrt(7). Multiply the coefficients together and the surd parts together. (5 × (2)/(5)) × (sqrt(7) × sqrt(7)) First, multiply the coefficients: 5 × (2)/(5) = (10)/(5) = 2 Next, multiply the surd parts: sqrt(7) × sqrt(7) = sqrt(7 × 7) = sqrt(49) = 7 Finally, multiply these two results: 2 × 7 = 14 14 Step 4: Simplify by expressing (3sqrt(2))^2 as a complete surd. To simplify (3sqrt(2))^2, square both the coefficient and the surd part. (3sqrt(2))^2 = 3^2 × (sqrt(2))^2 = 9 × 2 = 18 To express 18 as a complete surd, write it under a square root sign. 18 = sqrt(18^2) = sqrt(324) sqrt(324) What's next?