I am trying to cancel common factors under square roots in some expression with all positive real variables: $$\text{Simplify}\left[\frac{\left(3+\sqrt{6}\right) \sqrt{g} \text{nn}^4}{2 \sqrt{\text{nn}^7 P*T}},\text{nn}>0\land P>0\land T>0\right]$$
which returns the same thing $$\frac{\left(3+\sqrt{6}\right) \sqrt{g} \text{nn}^4}{2 \sqrt{\text{nn}^7 P T}}.$$
However, removing the assumptions for $P,T$ makes it work: $$\text{Simplify}\left[\frac{\left(3+\sqrt{6}\right) \sqrt{g} \text{nn}^4}{2 \sqrt{\text{nn}^7 P T}},\text{nn}>0\right]$$ $$\frac{\left(3+\sqrt{6}\right) \sqrt{g \text{nn}}}{2 \sqrt{P T}}.$$
Why does it happen? And a more important question, what is a better way to cancel common factors under roots with positive real variables in the more general case with larger expressions and many variables to cancel, so that I am sure no common factors remain?
