Cube Root of 1029
Cube Root Calculator
What is the cube root of 1,029?
Answer
∛1,029 =
7∛3 ≈ 10.0957
Real cube root: the only number whose cube is 1,029.
≈ — rounded to 4 decimal places. 1,029 is not the cube of a rational number, so ∛1,029 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,029 = 3 × (7 × 7 × 7) = 3 × 7³
- Take out of the root
- ∛1,029 = ∛(7³ × 3) = 7∛3
- Between cubes
- 10³ = 1,000 < 1,029 < 1,331 = 11³, so 10 < ∛1,029 < 11 and ∛1,029 ≈ 10.0957
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FAQ
What is the cube root of 1,029?
∛1,029 = 7∛3 ≈ 10.0957
How to simplify ∛1,029?
Factor 1,029 into primes: 1,029 = 3 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,029 = ∛(7³ × 3) = 7∛3.
Is ∛1,029 a rational number?
No: 1,029 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 ∛1,029 is irrational; its decimal never ends and never repeats: ∛1,029 ≈ 10.0957.
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