Cube Root of 10000

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What is the cube root of 10,000?

Answer

∛10,000 =
10∛10 ≈ 21.5443

Real cube root: the only number whose cube is 10,000.

≈ — rounded to 4 decimal places. 10,000 is not the cube of a rational number, so ∛10,000 is irrational: its decimal expansion never ends and never repeats.

Prime factors
10,000 = (2 × 2 × 2) × 2 × (5 × 5 × 5) × 5 = 2⁴ × 5⁴
Take out of the root
∛10,000 = ∛(2³ × 5³ × 10) = 2 × 5 × ∛10 = 10∛10
Between cubes
21³ = 9,261 < 10,000 < 10,648 = 22³, so 21 < ∛10,000 < 22 and ∛10,000 ≈ 21.5443

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
9,26121
9,621≈ 21.2687
9,999≈ 21.5436
10,00010∛10 ≈ 21.5443
10,36812∛6 ≈ 21.8054
10,64822
11,025≈ 22.2566

FAQ

What is the cube root of 10,000?

∛10,000 = 10∛10 ≈ 21.5443

How to simplify ∛10,000?

Factor 10,000 into primes: 10,000 = 2 × 2 × 2 × 2 × 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: ∛10,000 = ∛(2³ × 5³ × 10) = 10∛10.

Is ∛10,000 a rational number?

No: 10,000 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 ∛10,000 is irrational; its decimal never ends and never repeats: ∛10,000 ≈ 21.5443.

See Also