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 — Question 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 radicals for the first term. (7 × 2)sqrt(6 × 10) = 14sqrt(60) Step 3: Multiply the coefficients and the radicals for the second term. (7 × 5)sqrt(6 × 2) = 35sqrt(12) So the expression becomes: 14sqrt(60) - 35sqrt(12) Step 4: Simplify the radicals sqrt(60) and sqrt(12). For sqrt(60): sqrt(60) = sqrt(4 × 15) = sqrt(4) × sqrt(15) = 2sqrt(15) For sqrt(12): sqrt(12) = sqrt(4 × 3) = sqrt(4) × sqrt(3) = 2sqrt(3) Step 5: Substitute the simplified radicals back into the expression. 14(2sqrt(15)) - 35(2sqrt(3)) 28sqrt(15) - 70sqrt(3) The terms 28sqrt(15) and 70sqrt(3) are not like terms because their radical parts are different, so they cannot be combined further. The simplified product is 28sqrt(15) - 70sqrt(3). 28sqrt(15) - 70sqrt(3) What's next?