Cube Root of −81
Cube Root Calculator
What is the cube root of −81?
Answer
∛(−81) =
−3∛3 ≈ −4.3267
Real cube root: the only number whose cube is −81.
≈ — rounded to 4 decimal places. −81 is not the cube of a rational number, so ∛(−81) is irrational: its decimal expansion never ends and never repeats.
A negative number has a negative cube root: (−3∛3)³ = −81. There is no real square root of −81.
- Sign
- ∛(−81) = −∛81, because (−a)³ = −a³
- Prime factors
- 81 = (3 × 3 × 3) × 3 = 3⁴
- Take out of the root
- ∛81 = ∛(3³ × 3) = 3∛3
- Between cubes
- 4³ = 64 < 81 < 125 = 5³, so 4 < ∛81 < 5 and ∛81 ≈ 4.3267
Found an error in the calculation or the information?
Related Calculations
See Also
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
Share This Calculation
Print
<a href="https://calculat.io/en/number/cube-root/-81">Cube Root of −81 (∛(−81)): Exact Value and Decimal</a>Facebook
Twitter
Telegram
WhatsApp
Viber
Email
Cube roots of nearby values
| N | ∛N |
|---|---|
| −216 | −6 |
| −125 | −5 |
| −108 | −3∛4 ≈ −4.7622 |
| −81 | −3∛3 ≈ −4.3267 |
| −64 | −4 |
| −54 | −3∛2 ≈ −3.7798 |
| −49 | −∛49 ≈ −3.6593 |