Cube Root of 1210
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What is the cube root of 1,210?
Answer
∛1,210 ≈
10.656
Real cube root: the only number whose cube is 1,210.
≈ — rounded to 4 decimal places. 1,210 is not the cube of a rational number, so ∛1,210 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,210 = 2 × 5 × 11 × 11 = 2 × 5 × 11²
- Take out of the root
- No prime appears three times, so ∛1,210 is already in simplest form.
- Between cubes
- 10³ = 1,000 < 1,210 < 1,331 = 11³, so 10 < ∛1,210 < 11 and ∛1,210 ≈ 10.656
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- 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 1,210?
∛1,210 ≈ 10.656
Can ∛1,210 be simplified?
No: no prime appears three times in 1,210, so its only cube factor is 1 and ∛1,210 is already in simplest form. Since 10³ = 1,000 < 1,210 < 1,331 = 11³, ∛1,210 lies between 10 and 11: ∛1,210 ≈ 10.656.
Is ∛1,210 a rational number?
No: 1,210 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 ∛1,210 is irrational; its decimal never ends and never repeats: ∛1,210 ≈ 10.656.
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