Cube Root of 112
Cube Root Calculator
What is the cube root of 112?
Answer
∛112 =
2∛14 ≈ 4.8203
Real cube root: the only number whose cube is 112.
≈ — rounded to 4 decimal places. 112 is not the cube of a rational number, so ∛112 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 112 = (2 × 2 × 2) × 2 × 7 = 2⁴ × 7
- Take out of the root
- ∛112 = ∛(2³ × 14) = 2∛14
- Between cubes
- 4³ = 64 < 112 < 125 = 5³, so 4 < ∛112 < 5 and ∛112 ≈ 4.8203
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FAQ
What is the cube root of 112?
∛112 = 2∛14 ≈ 4.8203
How to simplify ∛112?
Factor 112 into primes: 112 = 2 × 2 × 2 × 2 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛112 = ∛(2³ × 14) = 2∛14.
Is ∛112 a rational number?
No: 112 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 ∛112 is irrational; its decimal never ends and never repeats: ∛112 ≈ 4.8203.
See Also
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