The square root of 200
Biology
ScanSolve AI Answer
Step-by-step solution
5 stepsLet's find the square root of 200.
Rewrite 200 as a product of its prime factors.
200 = 2 × 100 = 2 × 10 × 10 = 2 × (2 × 5) × (2 × 5) = 2³ × 5²
Apply the square root to the prime factorization.
√(200) = √(2³ × 5²)
Simplify the square root by taking out perfect squares.
√(2³ × 5²) = √(2² × 2 × 5²) = √(2²) × √(5²) × √(2)
Calculate the square roots of the perfect squares.
√(2²) = 2
√(5²) = 5Combine the results.
2 × 5 × √(2) = 10√(2)
The square root of 200 is 10√(2).
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