Cube Root of 1372
Cube Root Calculator
What is the cube root of 1,372?
Answer
∛1,372 =
7∛4 ≈ 11.1118
Real cube root: the only number whose cube is 1,372.
≈ — rounded to 4 decimal places. 1,372 is not the cube of a rational number, so ∛1,372 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,372 = 2 × 2 × (7 × 7 × 7) = 2² × 7³
- Take out of the root
- ∛1,372 = ∛(7³ × 4) = 7∛4
- Between cubes
- 11³ = 1,331 < 1,372 < 1,728 = 12³, so 11 < ∛1,372 < 12 and ∛1,372 ≈ 11.1118
See Also
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- 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 1,372?
∛1,372 = 7∛4 ≈ 11.1118
How to simplify ∛1,372?
Factor 1,372 into primes: 1,372 = 2 × 2 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,372 = ∛(7³ × 4) = 7∛4.
Is ∛1,372 a rational number?
No: 1,372 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 ∛1,372 is irrational; its decimal never ends and never repeats: ∛1,372 ≈ 11.1118.
See Also
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