Cube Root of 102
Cube Root Calculator
What is the cube root of 102?
Answer
∛102 ≈
4.6723
Real cube root: the only number whose cube is 102.
≈ — rounded to 4 decimal places. 102 is not the cube of a rational number, so ∛102 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 102 = 2 × 3 × 17
- Take out of the root
- No prime appears three times, so ∛102 is already in simplest form.
- Between cubes
- 4³ = 64 < 102 < 125 = 5³, so 4 < ∛102 < 5 and ∛102 ≈ 4.6723
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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 102?
∛102 ≈ 4.6723
Can ∛102 be simplified?
No: no prime appears three times in 102, so its only cube factor is 1 and ∛102 is already in simplest form. Since 4³ = 64 < 102 < 125 = 5³, ∛102 lies between 4 and 5: ∛102 ≈ 4.6723.
Is ∛102 a rational number?
No: 102 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 ∛102 is irrational; its decimal never ends and never repeats: ∛102 ≈ 4.6723.
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