Cube Root of 200
Cube Root Calculator
What is the cube root of 200?
Answer
∛200 =
2∛25 ≈ 5.848
Real cube root: the only number whose cube is 200.
≈ — rounded to 4 decimal places. 200 is not the cube of a rational number, so ∛200 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 200 = (2 × 2 × 2) × 5 × 5 = 2³ × 5²
- Take out of the root
- ∛200 = ∛(2³ × 25) = 2∛25
- Between cubes
- 5³ = 125 < 200 < 216 = 6³, so 5 < ∛200 < 6 and ∛200 ≈ 5.848
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FAQ
What is the cube root of 200?
∛200 = 2∛25 ≈ 5.848
How to simplify ∛200?
Factor 200 into primes: 200 = 2 × 2 × 2 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛200 = ∛(2³ × 25) = 2∛25.
Is ∛200 a rational number?
No: 200 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛200 is irrational; its decimal never ends and never repeats: ∛200 ≈ 5.848.
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