Cube Root of 3/5

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Cube root of

What is the cube root of 3/5?

Answer

∛(3/5) =
∛75/5 ≈ 0.8434

Real cube root: the only number whose cube is 3/5.

≈ — rounded to 4 decimal places. 3/5 is not the cube of a rational number, so ∛(3/5) is irrational: its decimal expansion never ends and never repeats.

Root of a fraction
∛(3/5) = ∛3/∛5
Multiply by ∛(5²) = ∛25
∛3/∛5 = ∛75/∛125 = ∛75/5 ≈ 0.8434

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
0.5120.8
64/1254/5 = 0.8
125/2165/6 ≈ 0.8333
3/5∛75/5 ≈ 0.8434
216/3436/7 ≈ 0.8571
2/3∛18/3 ≈ 0.8736
343/5127/8 = 0.875

FAQ

What is the cube root of 3/5?

∛(3/5) = ∛75/5 ≈ 0.8434

Why is ∛(3/5) = ∛75/5?

∛(3/5) = ∛3/∛5. Multiplying the numerator and the denominator by ∛(5²) = ∛25 makes the denominator a perfect cube: ∛75/∛125 = ∛75/5. The value does not change; only the root leaves the denominator.

Is ∛(3/5) a rational number?

No: 3/5 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 ∛(3/5) is irrational; its decimal never ends and never repeats: ∛(3/5) ≈ 0.8434.

See Also