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
Here's the solution for question 8. 8. Calculate the product: 7sqrt(6)(2sqrt(10) - 5sqrt(2)) Step 1: Distribute 7sqrt(6) to each term inside the parentheses. 7sqrt(6) · (2sqrt(10)) - 7sqrt(6) · (5sqrt(2)) Step 2: Multiply the coefficients and the terms under the square roots for each part. (7 · 2)sqrt(6 · 10) - (7 · 5)sqrt(6 · 2) 14sqrt(60) - 35sqrt(12) Step 3: Simplify the surds sqrt(60) and sqrt(12). sqrt(60) = sqrt(4 · 15) = sqrt(4) · sqrt(15) = 2sqrt(15) sqrt(12) = sqrt(4 · 3) = sqrt(4) · sqrt(3) = 2sqrt(3) Step 4: Substitute the simplified surds back into the expression. 14(2sqrt(15)) - 35(2sqrt(3)) Step 5: Perform the final multiplications. 28sqrt(15) - 70sqrt(3) The terms sqrt(15) and sqrt(3) are not like terms, so they cannot be combined further. 28sqrt(15) - 70sqrt(3) That's 2 down. 3 left today — send the next one.