Cube Root of 1001
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What is the cube root of 1,001?
Answer
∛1,001 ≈
10.0033
Real cube root: the only number whose cube is 1,001.
≈ — rounded to 4 decimal places. 1,001 is not the cube of a rational number, so ∛1,001 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,001 = 7 × 11 × 13
- Take out of the root
- No prime appears three times, so ∛1,001 is already in simplest form.
- Between cubes
- 10³ = 1,000 < 1,001 < 1,331 = 11³, so 10 < ∛1,001 < 11 and ∛1,001 ≈ 10.0033
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FAQ
What is the cube root of 1,001?
∛1,001 ≈ 10.0033
Can ∛1,001 be simplified?
No: no prime appears three times in 1,001, so its only cube factor is 1 and ∛1,001 is already in simplest form. Since 10³ = 1,000 < 1,001 < 1,331 = 11³, ∛1,001 lies between 10 and 11: ∛1,001 ≈ 10.0033.
Is ∛1,001 a rational number?
No: 1,001 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 ∛1,001 is irrational; its decimal never ends and never repeats: ∛1,001 ≈ 10.0033.
See Also
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