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
a) Step 1: Distribute sqrt(5) to each term inside the parenthesis. sqrt(5)(sqrt(2) + 1) = sqrt(5) × sqrt(2) + sqrt(5) × 1 Step 2: Multiply the surds and simplify. sqrt(5 × 2) + sqrt(5) = sqrt(10) + sqrt(5) The simplified expression is: sqrt(10) + sqrt(5) b) Step 1: Distribute sqrt(5) to each term inside the parenthesis. sqrt(5)(3 - sqrt(2)) = sqrt(5) × 3 - sqrt(5) × sqrt(2) Step 2: Multiply the terms. 3sqrt(5) - sqrt(5 × 2) = 3sqrt(5) - sqrt(10) The simplified expression is: 3sqrt(5) - sqrt(10) c) Step 1: Apply the exponent to both factors inside the parenthesis. (2sqrt(2))^3 = 2^3 × (sqrt(2))^3 Step 2: Calculate 2^3. 2^3 = 2 × 2 × 2 = 8 Step 3: Calculate (sqrt(2))^3. (sqrt(2))^3 = sqrt(2) × sqrt(2) × sqrt(2) = (sqrt(2))^2 × sqrt(2) = 2 × sqrt(2) = 2sqrt(2) Step 4: Multiply the results from Step 2 and Step 3. 8 × 2sqrt(2) = 16sqrt(2) The simplified expression is: 16sqrt(2) 3 done, 2 left today. You're making progress.