Cube Root of 289
Cube Root Calculator
What is the cube root of 289?
Answer
∛289 ≈
6.6115
Real cube root: the only number whose cube is 289.
≈ — rounded to 4 decimal places. 289 is not the cube of a rational number, so ∛289 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 289 = 17 × 17 = 17²
- Take out of the root
- No prime appears three times, so ∛289 is already in simplest form.
- Between cubes
- 6³ = 216 < 289 < 343 = 7³, so 6 < ∛289 < 7 and ∛289 ≈ 6.6115
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See Also
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
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FAQ
What is the cube root of 289?
∛289 ≈ 6.6115
Can ∛289 be simplified?
No: no prime appears three times in 289, so its only cube factor is 1 and ∛289 is already in simplest form. Since 6³ = 216 < 289 < 343 = 7³, ∛289 lies between 6 and 7: ∛289 ≈ 6.6115.
Is ∛289 a rational number?
No: 289 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 ∛289 is irrational; its decimal never ends and never repeats: ∛289 ≈ 6.6115.
See Also
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