How do you find the cube root of a negative number?

Answer 1

If the negative number is "-a", then you can say the cube root is "-(cube root of a)"

Because if you cube a negative number, you get a negative number. So if you cube root a negative number, you get a negative number.

Ex) cube root of -8 = -2

Because (-2)^3 = -8

But if you want to find the complex cube roots, you can make an equation:

"x^3=-a" or "x^3+a=0"

We know one of the roots is "-(cube root of a)" so you can factor the equation by (x+(cube root of a))

And then you use the quadratic formula for the quadratic equation you're left with.

Ex) x^3=-8 or x^3+8=0

Since -2 is a root, factor it by (x+2)

x^3+8=(x+2)(x^2-2x+4)

Using the quadratic formula, you get "1+i√3" and "1-i√3"

Therefore the three cube roots of -8 is <"-2", "1+i√3", "1-i√3">