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) Simplify 2sqrt(3)(2-sqrt(3)) + 2sqrt(2)(sqrt(2)-1) Step 1: Distribute 2sqrt(3) into the first parenthesis. 2sqrt(3)(2-sqrt(3)) = (2sqrt(3) × 2) - (2sqrt(3) × sqrt(3)) = 4sqrt(3) - 2(sqrt(3 × 3)) = 4sqrt(3) - 2(3) = 4sqrt(3) - 6 Step 2: Distribute 2sqrt(2) into the second parenthesis. 2sqrt(2)(sqrt(2)-1) = (2sqrt(2) × sqrt(2)) - (2sqrt(2) × 1) = 2(sqrt(2 × 2)) - 2sqrt(2) = 2(2) - 2sqrt(2) = 4 - 2sqrt(2) Step 3: Combine the simplified expressions. (4sqrt(3) - 6) + (4 - 2sqrt(2)) = 4sqrt(3) - 6 + 4 - 2sqrt(2) Combine the constant terms: = 4sqrt(3) - 2sqrt(2) - 2 The simplified expression is 4sqrt(3) - 2sqrt(2) - 2. b) Hence evaluate your answer in (a) correct to 2dp given that sqrt(2) = 1.414 and sqrt(3) = 1.732 Step 1: Substitute the given values of sqrt(2) and sqrt(3) into the simplified expression from part (a). 4sqrt(3) - 2sqrt(2) - 2 = 4(1.732) - 2(1.414) - 2 Step 2: Perform the multiplications. 4 × 1.732 = 6.928 2 × 1.414 = 2.828 Step 3: Perform the subtractions. 6.928 - 2.828 - 2 = 4.100 - 2 = 2.100 Step 4: Round the result to 2 decimal places. 2.100 ≈ 2.10 The evaluated answer is 2.10. 3 done, 2 left today. You're making progress.