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
The square root of a number is a value that, when multiplied by itself, gives the original number. Step 1: Find the prime factorization of 800. 800 = 8 × 100 = 2³ × 10² = 2³ × (2 × 5)² = 2³ × 2² × 5² = 2⁵ × 5² Step 2: Rewrite the square root using the prime factorization. √(800) = √(2⁵ × 5²) Step 3: Simplify the square root by taking out perfect squares. √(2⁵ × 5²) = √(2⁴ × 2¹ × 5²) = √(2⁴) × √(5²) × √(2) = 2² × 5 × √(2) Step 4: Calculate the final value. 2² × 5 × √(2) = 4 × 5 × √(2) = 20√(2) The square root of 800 is 20√(2). Send me the next one 📸