Cube Root of 336

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Cube root of

What is the cube root of 336?

Answer

∛336 =
2∛42 ≈ 6.9521

Real cube root: the only number whose cube is 336.

≈ — rounded to 4 decimal places. 336 is not the cube of a rational number, so ∛336 is irrational: its decimal expansion never ends and never repeats.

Prime factors
336 = (2 × 2 × 2) × 2 × 3 × 7 = 2⁴ × 3 × 7
Take out of the root
∛336 = ∛(2³ × 42) = 2∛42
Between cubes
6³ = 216 < 336 < 343 = 7³, so 6 < ∛336 < 7 and ∛336 ≈ 6.9521

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
329≈ 6.9034
330≈ 6.9104
331≈ 6.9174
3362∛42 ≈ 6.9521
3437
3755∛3 ≈ 7.2112
425≈ 7.5185

FAQ

What is the cube root of 336?

∛336 = 2∛42 ≈ 6.9521

How to simplify ∛336?

Factor 336 into primes: 336 = 2 × 2 × 2 × 2 × 3 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛336 = ∛(2³ × 42) = 2∛42.

Is ∛336 a rational number?

No: 336 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 ∛336 is irrational; its decimal never ends and never repeats: ∛336 ≈ 6.9521.

See Also