Cube Root of −32
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What is the cube root of −32?
Answer
∛(−32) =
−2∛4 ≈ −3.1748
Real cube root: the only number whose cube is −32.
≈ — rounded to 4 decimal places. −32 is not the cube of a rational number, so ∛(−32) is irrational: its decimal expansion never ends and never repeats.
A negative number has a negative cube root: (−2∛4)³ = −32. There is no real square root of −32.
- Sign
- ∛(−32) = −∛32, because (−a)³ = −a³
- Prime factors
- 32 = (2 × 2 × 2) × 2 × 2 = 2⁵
- Take out of the root
- ∛32 = ∛(2³ × 4) = 2∛4
- Between cubes
- 3³ = 27 < 32 < 64 = 4³, so 3 < ∛32 < 4 and ∛32 ≈ 3.1748
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Cube roots of nearby values
| N | ∛N |
|---|---|
| −64 | −4 |
| −54 | −3∛2 ≈ −3.7798 |
| −49 | −∛49 ≈ −3.6593 |
| −32 | −2∛4 ≈ −3.1748 |
| −27 | −3 |
| −25 | −∛25 ≈ −2.924 |
| −21 | −∛21 ≈ −2.7589 |