Cube Root of 117
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What is the cube root of 117?
Answer
∛117 ≈
4.891
Real cube root: the only number whose cube is 117.
≈ — rounded to 4 decimal places. 117 is not the cube of a rational number, so ∛117 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 117 = 3 × 3 × 13 = 3² × 13
- Take out of the root
- No prime appears three times, so ∛117 is already in simplest form.
- Between cubes
- 4³ = 64 < 117 < 125 = 5³, so 4 < ∛117 < 5 and ∛117 ≈ 4.891
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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 117?
∛117 ≈ 4.891
Can ∛117 be simplified?
No: no prime appears three times in 117, so its only cube factor is 1 and ∛117 is already in simplest form. Since 4³ = 64 < 117 < 125 = 5³, ∛117 lies between 4 and 5: ∛117 ≈ 4.891.
Is ∛117 a rational number?
No: 117 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 ∛117 is irrational; its decimal never ends and never repeats: ∛117 ≈ 4.891.
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