Cube Root of 243

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Cube root of

What is the cube root of 243?

Answer

∛243 =
3∛9 ≈ 6.2403

Real cube root: the only number whose cube is 243.

≈ — rounded to 4 decimal places. 243 is not the cube of a rational number, so ∛243 is irrational: its decimal expansion never ends and never repeats.

Prime factors
243 = (3 × 3 × 3) × 3 × 3 = 3⁵
Take out of the root
∛243 = ∛(3³ × 9) = 3∛9
Between cubes
6³ = 216 < 243 < 343 = 7³, so 6 < ∛243 < 7 and ∛243 ≈ 6.2403

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
239≈ 6.2058
2402∛30 ≈ 6.2145
242≈ 6.2317
2433∛9 ≈ 6.2403
245≈ 6.2573
247≈ 6.2743
2482∛31 ≈ 6.2828

FAQ

What is the cube root of 243?

∛243 = 3∛9 ≈ 6.2403

How to simplify ∛243?

Factor 243 into primes: 243 = 3 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛243 = ∛(3³ × 9) = 3∛9.

Is ∛243 a rational number?

No: 243 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 ∛243 is irrational; its decimal never ends and never repeats: ∛243 ≈ 6.2403.

See Also