What are the cube roots of 8?

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Answer 1 · 2018-03-04T16:12:21

Solve #x^3-8 = 0#

Use either known factoring #a^3-b^3 = (a-b)(a^2+ab+b^2)# or divide #x^3-8# by #x-2# to find the quedratic factor.

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

#x^3-8 = 0# if and only if

#x-2 = 0# or #x^2+2x+4 = 0#

So one solution is #2#

The quadratic may be solved by completing the square of by formula

#x = (-(2)+-sqrt((2)^2-4(1)(4)))/(2(1))#

# = -1+-isqrt3#