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What is the cube root of 1,458?

Answer

∛1,458 =
9∛2 ≈ 11.3393

Real cube root: the only number whose cube is 1,458.

≈ — rounded to 4 decimal places. 1,458 is not the cube of a rational number, so ∛1,458 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,458 = 2 × (3 × 3 × 3) × (3 × 3 × 3) = 2 × 3⁶
Take out of the root
∛1,458 = ∛((3³)² × 2) = 3² × ∛2 = 9∛2
Between cubes
11³ = 1,331 < 1,458 < 1,728 = 12³, so 11 < ∛1,458 < 12 and ∛1,458 ≈ 11.3393

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,332≈ 11.0028
1,369≈ 11.1037
1,3727∛4 ≈ 11.1118
1,4589∛2 ≈ 11.3393
1,4882∛186 ≈ 11.4165
1,521≈ 11.5003
1,5368∛3 ≈ 11.538

FAQ

What is the cube root of 1,458?

∛1,458 = 9∛2 ≈ 11.3393

How to simplify ∛1,458?

Factor 1,458 into primes: 1,458 = 2 × 3 × 3 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,458 = ∛((3³)² × 2) = 9∛2.

Is ∛1,458 a rational number?

No: 1,458 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 ∛1,458 is irrational; its decimal never ends and never repeats: ∛1,458 ≈ 11.3393.

See Also