I was working on a problem to find the degree of the splitting field of the polynomial x^3-11 over Q
I figured out to some extent. x^3-11 =0 has roots r*1,r*w,r*w^2 as roots where r is the cubic root of 11; w and w^2 are the cubic roots of unity.
I realize that the w cannot belong to Q as it is complex. My doubt is with the degree of the splitting field. I've got the answer for the degree to be 6.
Can anyone give a brief explanation of how it is 6?
Thanks,
MAX