Because the cube of a positive number is positive and the cube of a negative number is negative.

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Every number has THREE cube roots. However, (at least) two of the three are complex numbers.

For example, the cube roots of 8 are 2, (-1 + √3 i) and (-1 - √3 i) with i² = -1:

2³ = 2 × 2 × 2 = 8

(-1 + √3 i)³ = (-1 + √3 i)(-1 + √3 i)(-1 + √3 i)

= (-1 + √3 i)((-1)² - 2√3 i + 3i²)

= (-1 + √3 i)(1 - 2√3 i -3)

= (-1 + √3 i)(-2 - 2√3 i)

= (-1 + √3 i)(-1 - √3 i)2

= ((-1)² - 3i²)2

= (1 + 3)2

= 4 × 2 = 8

(-1 - √3 i)³ = (-1 - √3 i)(-1 - √3 i)(-1 - √3 i)

= (-1 - √3 i)((-1)² + 2√3 i + 3i²)

= (-1 - √3 i)(1 + 2√3 i -3)

= (-1 - √3 i)(-2 + 2√3 i)

= (-1 - √3 i)(-1 + √3 i)2

= ((-1)² - 3i²)2

= (1 + 3)2

= 4 × 2 = 8