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 5e. 5e) Step 1: Simplify the first term, sqrt((27x^4)/(3)). sqrt((27x^4)/(3)) = sqrt(9x^4) sqrt(9x^4) = sqrt(9) · sqrt(x^4) = 3x^2 Step 2: Simplify the second term, 3/(27). 3/(27) = 3/(9) 3/(9) = [3]x^6[3]9 = (x^2)/([3]9) To rationalize the denominator, multiply the numerator and denominator by [3]3: (x^2)/([3]9) · [3]3[3]3 = x^2[3]3[3]27 = x^2[3]33 Step 3: Simplify the third term, sqrt((x^5)/(x)). sqrt((x^5)/(x)) = sqrt(x^5-1) = sqrt(x^4) sqrt(x^4) = x^2 Step 4: Combine all the simplified terms. 3x^2 + x^2[3]33 - x^2 Combine the like terms (3x^2 - x^2): (3x^2 - x^2) + x^2[3]33 = 2x^2 + x^2[3]33 The final answer is 2x^2 + x^2[3]33. 3 done, 2 left today. You're making progress.