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
Step 1: Find the prime factors of 729. We divide 729 by the smallest prime number, which is 3. 729 ÷ 3 = 243 243 ÷ 3 = 81 81 ÷ 3 = 27 27 ÷ 3 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1 So, the prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3. Step 2: Group the prime factors into sets of three. To find the cube root, we group the identical prime factors in sets of three. 729 = (3 × 3 × 3) × (3 × 3 × 3) 729 = 3^3 × 3^3 Step 3: Calculate the cube root. [3]729 = [3]3^3 × 3^3 [3]729 = 3 × 3 [3]729 = 9 The cube root of 729 is 9. 9 Send me the next one 📸