Find the radical of the parabolic group

Question

Let's consider special linear group $SL(3)$. And we know one of its parabolic groups is $$P=\begin{bmatrix} * & * & * \\ * & * & * \\ 0 & 0 & * \end{bmatrix} $$where $*$ is any element in the ground field. Then we have to find the radical of $P$. From definition, radical is the connected component through identity element of intersection of all the Borel subgroups of $P$. Is there any good way to find radical? Or we have to find out all the Borel subgroups and connected components of their intersection. One of the Borel subgroup is upper triangular matrices in $SL(3)$. I'm not so clear that how may conjugate groups of this Borel group we have.