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What is the cube root of 1,488?

Answer

∛1,488 =
2∛186 ≈ 11.4165

Real cube root: the only number whose cube is 1,488.

≈ — rounded to 4 decimal places. 1,488 is not the cube of a rational number, so ∛1,488 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,488 = (2 × 2 × 2) × 2 × 3 × 31 = 2⁴ × 3 × 31
Take out of the root
∛1,488 = ∛(2³ × 186) = 2∛186
Between cubes
11³ = 1,331 < 1,488 < 1,728 = 12³, so 11 < ∛1,488 < 12 and ∛1,488 ≈ 11.4165

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
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
1,700≈ 11.9348

FAQ

What is the cube root of 1,488?

∛1,488 = 2∛186 ≈ 11.4165

How to simplify ∛1,488?

Factor 1,488 into primes: 1,488 = 2 × 2 × 2 × 2 × 3 × 31. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,488 = ∛(2³ × 186) = 2∛186.

Is ∛1,488 a rational number?

No: 1,488 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 ∛1,488 is irrational; its decimal never ends and never repeats: ∛1,488 ≈ 11.4165.

See Also