Eigenvalues of a 6x6 matrix

Question

Eigenvalues[{{0, A, 0, B, 0, D}, {-A, 0, -C, 0, -EE, 0}, {0, C, 0, A, 
    0, B}, {-B, 0, -A, 0, -C, 0}, {0, EE, 0, C, 0, A}, {-D, 0, -B, 
    0, -A, 0}}]

I am trying to get the eigenvalues of above matrix in algebraic form, however, the eigenvalues look like below:

-\[Sqrt]Root[
   A^6 - 4 A^4 B CC + 4 A^2 B^2 CC^2 + 2 A^3 CC^2 DD - 4 A B CC^3 DD +
      CC^4 DD^2 + 2 A^3 B^2 EE - 4 A B^3 CC EE - 2 A^4 DD EE + 
     4 A^2 B CC DD EE + 2 B^2 CC^2 DD EE - 2 A CC^2 DD^2 EE + 
     B^4 EE^2 - 2 A B^2 DD EE^2 + 
     A^2 DD^2 EE^2 + (3 A^4 + 2 A^2 B^2 + B^4 - 4 A^2 B CC + 
        2 A^2 CC^2 + 2 B^2 CC^2 + CC^4 - 2 A B^2 DD - 4 A B CC DD + 
        A^2 DD^2 + 2 CC^2 DD^2 - 4 A B CC EE - 2 A CC^2 EE - 
        2 A^2 DD EE + A^2 EE^2 + 2 B^2 EE^2 + 
        DD^2 EE^2) #1 + (3 A^2 + 2 B^2 + 2 CC^2 + DD^2 + 
        EE^2) #1^2 + #1^3 &, 1]

I don't quite understand the meaning of this expression. Do I need to solve this Root equation -Sqrt{f(#1)} = 0 ? How can I get a normal algebraic expressions for the eigenvalues?