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 — here's the solution for number 19. 19) Step 1: Express 1728 in terms of its prime factors. 1728 = 2 × 864 = 2^2 × 432 = 2^3 × 216 = 2^4 × 108 = 2^5 × 54 = 2^6 × 27 = 2^6 × 3^3 Step 2: Express 2025 in terms of its prime factors. 2025 = 5 × 405 = 5^2 × 81 = 5^2 × 3^4 Step 3: Substitute the prime factorizations into the expression sqrt((1728)/(2025)). sqrt((1728)/(2025)) = sqrt((2^6 × 3^3)/(3^4 × 5^2)) Step 4: Simplify the expression under the square root. sqrt((2^6 × 3^3)/(3^4 × 5^2)) = sqrt((2^6)/(3^4-3) × 5^2) = sqrt((2^6)/(3^1 × 5^2)) = sqrt(2^6)sqrt(3 × 5^2) = 2^6/2sqrt(3) × 5^2/2 = (2^3)/(5sqrt(3)) = (8)/(5sqrt(3)) Step 5: Rationalize the denominator. (8)/(5sqrt(3)) × sqrt(3)sqrt(3) = 8sqrt(3)5 × 3 = 8sqrt(3)15 8sqrt(3)15 You've got 2 more questions today. What's next?