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 factorization of 7744. Divide 7744 by the smallest prime numbers until the quotient is 1. 7744 ÷ 2 &= 3872 \\ 3872 ÷ 2 &= 1936 \\ 1936 ÷ 2 &= 968 \\ 968 ÷ 2 &= 484 \\ 484 ÷ 2 &= 242 \\ 242 ÷ 2 &= 121 \\ 121 ÷ 11 &= 11 \\ 11 ÷ 11 &= 1 So, the prime factorization of 7744 is 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11. Step 2: Group the prime factors into pairs. 7744 = (2 × 2) × (2 × 2) × (2 × 2) × (11 × 11) Step 3: Take one factor from each pair and multiply them to find the square root. sqrt(7744) = 2 × 2 × 2 × 11 sqrt(7744) = 8 × 11 sqrt(7744) = 88 The square root of 7744 is 88. That's 3 down. 2 left today — send the next one.