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
Let's simplify sqrt(2)(sqrt(6) + 2sqrt(2)) - 2sqrt(3) step by step. Step 1: Distribute sqrt(2) into the parenthesis. sqrt(2)(sqrt(6) + 2sqrt(2)) = sqrt(2) × sqrt(6) + sqrt(2) × 2sqrt(2) Step 2: Simplify the products. sqrt(2) × sqrt(6) = sqrt(12) sqrt(2) × 2sqrt(2) = 2 × (sqrt(2) × sqrt(2)) = 2 × 2 = 4 So the expression becomes: sqrt(12) + 4 - 2sqrt(3) Step 3: Simplify sqrt(12). sqrt(12) = sqrt(4 × 3) = sqrt(4) × sqrt(3) = 2sqrt(3) Step 4: Substitute the simplified term back into the expression. 2sqrt(3) + 4 - 2sqrt(3) Step 5: Combine like terms. (2sqrt(3) - 2sqrt(3)) + 4 = 0 + 4 = 4 The final answer is 4. 3 done, 2 left today. You're making progress.