Solving recurrences (tree method) with square roots
$n^2 \cdot \sqrt{n} = n^{5/2}$, then you can proceed with the Master Theorem as normal.

If you specifically need to use the Recursion Tree Method for solving recurrences, then you can still proceed normally.


Root Level : $n^{5/2}$
Next Level : $4 \cdot (n\ /\ 2)^{5/2} = 2^{4/2} \cdot n^{5/2}\ /\  2^{5/2} = n^{5/2}\ /\ 2^{1/2}$
Next Level : $16 \cdot (n\ /\ 4)^{5/2} = 4^{4/2} \cdot n^{5/2}\ /\ 4^{5/2} = n^{5/2}\ /\ 4^{1/2}$
etc.