Cube Root of 240
Cube Root Calculator
What is the cube root of 240?
Answer
∛240 =
2∛30 ≈ 6.2145
Real cube root: the only number whose cube is 240.
≈ — rounded to 4 decimal places. 240 is not the cube of a rational number, so ∛240 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 240 = (2 × 2 × 2) × 2 × 3 × 5 = 2⁴ × 3 × 5
- Take out of the root
- ∛240 = ∛(2³ × 30) = 2∛30
- Between cubes
- 6³ = 216 < 240 < 343 = 7³, so 6 < ∛240 < 7 and ∛240 ≈ 6.2145
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FAQ
What is the cube root of 240?
∛240 = 2∛30 ≈ 6.2145
How to simplify ∛240?
Factor 240 into primes: 240 = 2 × 2 × 2 × 2 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛240 = ∛(2³ × 30) = 2∛30.
Is ∛240 a rational number?
No: 240 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 ∛240 is irrational; its decimal never ends and never repeats: ∛240 ≈ 6.2145.
See Also
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- Cube Root of 223 (∛223): Exact Value and Decimal
- Cube Root of 225 (∛225): Exact Value and Decimal
- Cube Root of 228 (∛228): Exact Value and Decimal
- Cube Root of 230 (∛230): Exact Value and Decimal
- Cube Root of 231 (∛231): Exact Value and Decimal
- Cube Root of 233 (∛233): Exact Value and Decimal
- Cube Root of 238 (∛238): Exact Value and Decimal
- Cube Root of 239 (∛239): Exact Value and Decimal
- Cube Root of 242 (∛242): Exact Value and Decimal
- Cube Root of 243 (∛243): Exact Value and Decimal
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