Cube Root of 1/25

Cube Root Calculator
Cube root of

What is the cube root of 1/25?

Answer

∛(1/25) =
∛5/5 ≈ 0.342

Real cube root: the only number whose cube is 1/25.

≈ — rounded to 4 decimal places. 1/25 is not the cube of a rational number, so ∛(1/25) is irrational: its decimal expansion never ends and never repeats.

1/25 = 0.04.

Root of a fraction
∛(1/25) = ∛1/∛25 = 1/∛25
Multiply by ∛(25²) = ∛625
1/∛25 = ∛625/∛15,625 = ∛625/25
Take out of the root
∛625/25 = ∛(5³ × 5)/25 = 5∛5/25 = ∛5/5 ≈ 0.342

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
27/10003/10 = 0.3
1/271/3 ≈ 0.3333
0.04≈ 0.342
1/25∛5/5 ≈ 0.342
27/5123/8 = 0.375
0.0640.4
8/1252/5 = 0.4

FAQ

What is the cube root of 1/25?

∛(1/25) = ∛5/5 ≈ 0.342

Why is ∛(1/25) = ∛5/5?

∛(1/25) = ∛1/∛25. Multiplying the numerator and the denominator by ∛(25²) = ∛625 makes the denominator a perfect cube: ∛625/∛15,625 = ∛625/25. Taking the cubes out of ∛625 and reducing gives ∛5/5. The value does not change; only the root leaves the denominator.

Is ∛(1/25) a rational number?

No: 1/25 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 ∛(1/25) is irrational; its decimal never ends and never repeats: ∛(1/25) ≈ 0.342.

See Also