The minimum degree of a polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27}, \sqrt{2}+5 i$ as two of its roots is

The polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27}, \sqrt{2}+5 i$ as two roots. Then, other roots are $$ \begin{aligned} & \sqrt{3}-\sqrt{27} \text { and } \sqrt{2}-5 i \\ & -\sqrt{3}+\sqrt{27} \text { and }-\sqrt{3}-\sqrt{27} \end{aligned} $$ Therefore, number of roots are 6 and the minimum degree of a polynomial equation having 6 distinct roots is 6 .