Cube Root of 135

Cube Root Calculator
Cube root of

What is the cube root of 135?

Answer

∛135 =
3∛5 ≈ 5.1299

Real cube root: the only number whose cube is 135.

≈ — rounded to 4 decimal places. 135 is not the cube of a rational number, so ∛135 is irrational: its decimal expansion never ends and never repeats.

Prime factors
135 = (3 × 3 × 3) × 5 = 3³ × 5
Take out of the root
∛135 = ∛(3³ × 5) = 3∛5
Between cubes
5³ = 125 < 135 < 216 = 6³, so 5 < ∛135 < 6 and ∛135 ≈ 5.1299

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
129≈ 5.0528
131≈ 5.0788
132≈ 5.0916
1353∛5 ≈ 5.1299
1362∛17 ≈ 5.1426
137≈ 5.1551
142≈ 5.2171

FAQ

What is the cube root of 135?

∛135 = 3∛5 ≈ 5.1299

How to simplify ∛135?

Factor 135 into primes: 135 = 3 × 3 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛135 = ∛(3³ × 5) = 3∛5.

Is ∛135 a rational number?

No: 135 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 ∛135 is irrational; its decimal never ends and never repeats: ∛135 ≈ 5.1299.

See Also