Cube Root of 3087

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What is the cube root of 3,087?

Answer

∛3,087 =
7∛9 ≈ 14.5606

Real cube root: the only number whose cube is 3,087.

≈ — rounded to 4 decimal places. 3,087 is not the cube of a rational number, so ∛3,087 is irrational: its decimal expansion never ends and never repeats.

Prime factors
3,087 = 3 × 3 × (7 × 7 × 7) = 3² × 7³
Take out of the root
∛3,087 = ∛(7³ × 9) = 7∛9
Between cubes
14³ = 2,744 < 3,087 < 3,375 = 15³, so 14 < ∛3,087 < 15 and ∛3,087 ≈ 14.5606

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,74414
2,8804∛45 ≈ 14.2276
2,917≈ 14.2882
3,0877∛9 ≈ 14.5606
3,1255∛25 ≈ 14.6201
3,1364∛49 ≈ 14.6372
3,37515

FAQ

What is the cube root of 3,087?

∛3,087 = 7∛9 ≈ 14.5606

How to simplify ∛3,087?

Factor 3,087 into primes: 3,087 = 3 × 3 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛3,087 = ∛(7³ × 9) = 7∛9.

Is ∛3,087 a rational number?

No: 3,087 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 ∛3,087 is irrational; its decimal never ends and never repeats: ∛3,087 ≈ 14.5606.

See Also