Cube Root of 213
Cube Root Calculator
What is the cube root of 213?
Answer
∛213 ≈
5.9721
Real cube root: the only number whose cube is 213.
≈ — rounded to 4 decimal places. 213 is not the cube of a rational number, so ∛213 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 213 = 3 × 71
- Take out of the root
- No prime appears three times, so ∛213 is already in simplest form.
- Between cubes
- 5³ = 125 < 213 < 216 = 6³, so 5 < ∛213 < 6 and ∛213 ≈ 5.9721
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- 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 213?
∛213 ≈ 5.9721
Can ∛213 be simplified?
No: no prime appears three times in 213, so its only cube factor is 1 and ∛213 is already in simplest form. Since 5³ = 125 < 213 < 216 = 6³, ∛213 lies between 5 and 6: ∛213 ≈ 5.9721.
Is ∛213 a rational number?
No: 213 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 ∛213 is irrational; its decimal never ends and never repeats: ∛213 ≈ 5.9721.
See Also
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