Cube Root of 3136

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What is the cube root of 3,136?

Answer

∛3,136 =
4∛49 ≈ 14.6372

Real cube root: the only number whose cube is 3,136.

≈ — rounded to 4 decimal places. 3,136 is not the cube of a rational number, so ∛3,136 is irrational: its decimal expansion never ends and never repeats.

Prime factors
3,136 = (2 × 2 × 2) × (2 × 2 × 2) × 7 × 7 = 2⁶ × 7²
Take out of the root
∛3,136 = ∛((2³)² × 49) = 2² × ∛49 = 4∛49
Between cubes
14³ = 2,744 < 3,136 < 3,375 = 15³, so 14 < ∛3,136 < 15 and ∛3,136 ≈ 14.6372

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,917≈ 14.2882
3,0877∛9 ≈ 14.5606
3,1255∛25 ≈ 14.6201
3,1364∛49 ≈ 14.6372
3,37515
3,8886∛18 ≈ 15.7244
4,045≈ 15.9333

FAQ

What is the cube root of 3,136?

∛3,136 = 4∛49 ≈ 14.6372

How to simplify ∛3,136?

Factor 3,136 into primes: 3,136 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛3,136 = ∛((2³)² × 49) = 4∛49.

Is ∛3,136 a rational number?

No: 3,136 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 ∛3,136 is irrational; its decimal never ends and never repeats: ∛3,136 ≈ 14.6372.

See Also