now lidl (1 - W+'+(+-00)Find the cube roots of 8.

1.	now lidl (1 - W+'+(+-00)Find the cube roots of 8.
Answer» 8=2×2×2Therefore cubic root of 8 is 2 The cube roots of8are2,2ωand2ω2whereω=−12+√32iis the primitive Complex cube root of1. Explanation: Here are the cube roots of8plotted in the Complex plane on the circle of radius2: They can be written as: 2(cos(0)+isin(0))=2 2(cos(2π3)+isin(2π/3))=−1+√3i=2ω 2(cos(4π3)+isin(4π/3))=−1−√3i=2ω2 One way of finding these cube roots of8is to find all of the roots ofx3−8=0. x3−8=(x−2)(x2+2x+4) The quadratic factor can be solved usingthe quadratic formula: x=(−b±√(b²−4ac))/2a =−2±√22−(4×1×4)/2⋅1 =−2±√−122 =−1±√3

Answer»

8=2×2×2Therefore cubic root of 8 is 2

The cube roots of8are2,2ωand2ω2whereω=−12+√32iis the primitive Complex cube root of1.

Explanation:

Here are the cube roots of8plotted in the Complex plane on the circle of radius2:

They can be written as:

2(cos(0)+isin(0))=2

2(cos(2π3)+isin(2π/3))=−1+√3i=2ω

2(cos(4π3)+isin(4π/3))=−1−√3i=2ω2

One way of finding these cube roots of8is to find all of the roots ofx3−8=0.

x3−8=(x−2)(x2+2x+4)

The quadratic factor can be solved usingthe quadratic formula:

x=(−b±√(b²−4ac))/2a

=−2±√22−(4×1×4)/2⋅1

=−2±√−122

=−1±√3

Discussion