Cube Root of 81
Cube Root Calculator
What is the cube root of 81?
Answer
∛81 =
3∛3 ≈ 4.3267
Real cube root: the only number whose cube is 81.
≈ — rounded to 4 decimal places. 81 is not the cube of a rational number, so ∛81 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 81 = (3 × 3 × 3) × 3 = 3⁴
- Take out of the root
- ∛81 = ∛(3³ × 3) = 3∛3
- Between cubes
- 4³ = 64 < 81 < 125 = 5³, so 4 < ∛81 < 5 and ∛81 ≈ 4.3267
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FAQ
What is the cube root of 81?
∛81 = 3∛3 ≈ 4.3267
How to simplify ∛81?
Factor 81 into primes: 81 = 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛81 = ∛(3³ × 3) = 3∛3.
Is ∛81 a rational number?
No: 81 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 ∛81 is irrational; its decimal never ends and never repeats: ∛81 ≈ 4.3267.
See Also
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