Cube Root of 144
Cube Root Calculator
What is the cube root of 144?
Answer
∛144 =
2∛18 ≈ 5.2415
Real cube root: the only number whose cube is 144.
≈ — rounded to 4 decimal places. 144 is not the cube of a rational number, so ∛144 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 144 = (2 × 2 × 2) × 2 × 3 × 3 = 2⁴ × 3²
- Take out of the root
- ∛144 = ∛(2³ × 18) = 2∛18
- Between cubes
- 5³ = 125 < 144 < 216 = 6³, so 5 < ∛144 < 6 and ∛144 ≈ 5.2415
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FAQ
What is the cube root of 144?
∛144 = 2∛18 ≈ 5.2415
How to simplify ∛144?
Factor 144 into primes: 144 = 2 × 2 × 2 × 2 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛144 = ∛(2³ × 18) = 2∛18.
Is ∛144 a rational number?
No: 144 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 ∛144 is irrational; its decimal never ends and never repeats: ∛144 ≈ 5.2415.
See Also
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