Cube Root of −3
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What is the cube root of −3?
Answer
∛(−3) =
−∛3 ≈ −1.4422
Real cube root: the only number whose cube is −3.
≈ — rounded to 4 decimal places. −3 is not the cube of a rational number, so ∛(−3) is irrational: its decimal expansion never ends and never repeats.
A negative number has a negative cube root: (−∛3)³ = −3. There is no real square root of −3.
- Sign
- ∛(−3) = −∛3, because (−a)³ = −a³
- Prime factors
- 3 is a prime number: no triple of equal factors.
- Between cubes
- 1³ = 1 < 3 < 8 = 2³, so 1 < ∛3 < 2 and ∛3 ≈ 1.4422
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Cube roots of nearby values
| N | ∛N |
|---|---|
| −8 | −2 |
| −7 | −∛7 ≈ −1.9129 |
| −5 | −∛5 ≈ −1.71 |
| −3 | −∛3 ≈ −1.4422 |
| −2 | −∛2 ≈ −1.2599 |
| −1 | −1 |
| −0.5 | ≈ −0.7937 |