The square root of mean square speed is called root-square speed or rms speed. It is denoted by the symbol `v_(rms)`, Thus,

`v_(rms)=sqrt((Sigmav^2)/N)`

or, `v^2=v_(rms)^2`

We know, `p=1/3rhov^2.....(1)`

Equation (I) may be written as

`p=1/3rhov_(rms)^2`

so that `v_(rms)=sqrt((3p)/rho)=sqrt((3pV)/M)=sqrt((3RT)/M)`

`M->` molecular weight

`text(Avg. speed)` `v_(avg)=sqrt((8KT)/(pim_0))=sqrt((8RT)/(piM))`

`text(Most probable speed)` `v_p=sqrt((2KT)/(m_0))=sqrt((2KT)/(M))`