Cube Root of 3125

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What is the cube root of 3,125?

Answer

∛3,125 =
5∛25 ≈ 14.6201

Real cube root: the only number whose cube is 3,125.

≈ — rounded to 4 decimal places. 3,125 is not the cube of a rational number, so ∛3,125 is irrational: its decimal expansion never ends and never repeats.

Prime factors
3,125 = (5 × 5 × 5) × 5 × 5 = 5⁵
Take out of the root
∛3,125 = ∛(5³ × 25) = 5∛25
Between cubes
14³ = 2,744 < 3,125 < 3,375 = 15³, so 14 < ∛3,125 < 15 and ∛3,125 ≈ 14.6201

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
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
3,8886∛18 ≈ 15.7244

FAQ

What is the cube root of 3,125?

∛3,125 = 5∛25 ≈ 14.6201

How to simplify ∛3,125?

Factor 3,125 into primes: 3,125 = 5 × 5 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛3,125 = ∛(5³ × 25) = 5∛25.

Is ∛3,125 a rational number?

No: 3,125 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 ∛3,125 is irrational; its decimal never ends and never repeats: ∛3,125 ≈ 14.6201.

See Also