What is the square roots of 800
Mathematics
ScanSolve AI Answer
Answer
The square root of a number is a value that, when multiplied by itself, gives the original number.
Step-by-step solution
4 stepsFind the prime factorization of 800.
800 = 8 × 100 = 2³ × 10² = 2³ × (2 × 5)² = 2³ × 2² × 5² = 2⁵ × 5²
Rewrite the square root using the prime factorization.
√(800) = √(2⁵ × 5²)
Simplify the square root by taking out perfect squares.
√(2⁵ × 5²) = √(2⁴ × 2¹ × 5²) = √(2⁴) × √(5²) × √(2) = 2² × 5 × √(2)
Calculate the final value.
2² × 5 × √(2) = 4 × 5 × √(2) = 20√(2)
The square root of 800 is 20√(2).
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