The root mean square of speed of a gaseous molecules is given by $u_{\mathrm{rms}}=\sqrt{3p/\rho }$ This shows that a given temperature 

The gaseous molecule's root mean square velocity is expressed as

 $$\begin{gathered} \mu =\sqrt{\frac{3RT}{Mw}} \\ \mu =\sqrt{\frac{3p{V}_M}{Mw}} \\ \mu =\sqrt{\frac{3p}{p}} \end{gathered}$$

where $\mathrm{p}=\mathrm{Mw}/{\mathrm{V}}_m$

The root mean square varies as $\sqrt{\frac{p}{\rho }}$

and not on $\sqrt{p}$ and $\sqrt{\frac{1}{\rho }}$and at given temperature the ratio of 

remains constant. Therefore, 

$\mu =\sqrt{p{V}_m}$

Since $\mu =\sqrt{p{V}_m}$ .