Cube Root of −49
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What is the cube root of −49?
Answer
∛(−49) =
−∛49 ≈ −3.6593
Real cube root: the only number whose cube is −49.
≈ — rounded to 4 decimal places. −49 is not the cube of a rational number, so ∛(−49) is irrational: its decimal expansion never ends and never repeats.
A negative number has a negative cube root: (−∛49)³ = −49. There is no real square root of −49.
- Sign
- ∛(−49) = −∛49, because (−a)³ = −a³
- Prime factors
- 49 = 7 × 7 = 7²
- Take out of the root
- No prime appears three times, so ∛49 is already in simplest form.
- Between cubes
- 3³ = 27 < 49 < 64 = 4³, so 3 < ∛49 < 4 and ∛49 ≈ 3.6593
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Cube roots of nearby values
| N | ∛N |
|---|---|
| −81 | −3∛3 ≈ −4.3267 |
| −64 | −4 |
| −54 | −3∛2 ≈ −3.7798 |
| −49 | −∛49 ≈ −3.6593 |
| −32 | −2∛4 ≈ −3.1748 |
| −27 | −3 |
| −25 | −∛25 ≈ −2.924 |