The relationship among most probable velocity, average velocity and root mean Square velocity is respectively 

${\mathrm{U}}_{\mathrm{mp}} = \sqrt{(2\mathrm{RT}/\mathrm{M})}$

${\mathrm{U}}_{\mathrm{av}} = \sqrt{(8\mathrm{RT}/\mathrm{\pi M})}$

${\mathrm{U}}_{\mathrm{rms}}=\sqrt{(3\mathrm{RT}/\mathrm{M})}$

$$\begin{gathered} {\mathrm{U}}_{\mathrm{mp}} : {\mathrm{U}}_{\mathrm{av}} : {\mathrm{U}}_{\mathrm{rms}} = \sqrt{(2\mathrm{RT}/\mathrm{M})} : \sqrt{(8\mathrm{RT}/\mathrm{\pi M})} : \sqrt{(3\mathrm{RT}/\mathrm{M})} \\ = \sqrt{2} : \sqrt{(8/\pi )} : \sqrt{3} \end{gathered}$$