Cube Root of 48
Cube Root Calculator
What is the cube root of 48?
Answer
∛48 =
2∛6 ≈ 3.6342
Real cube root: the only number whose cube is 48.
≈ — rounded to 4 decimal places. 48 is not the cube of a rational number, so ∛48 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 48 = (2 × 2 × 2) × 2 × 3 = 2⁴ × 3
- Take out of the root
- ∛48 = ∛(2³ × 6) = 2∛6
- Between cubes
- 3³ = 27 < 48 < 64 = 4³, so 3 < ∛48 < 4 and ∛48 ≈ 3.6342
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FAQ
What is the cube root of 48?
∛48 = 2∛6 ≈ 3.6342
How to simplify ∛48?
Factor 48 into primes: 48 = 2 × 2 × 2 × 2 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛48 = ∛(2³ × 6) = 2∛6.
Is ∛48 a rational number?
No: 48 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 ∛48 is irrational; its decimal never ends and never repeats: ∛48 ≈ 3.6342.
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