Explain root mean square speed `(C or U_(rms))`

Explanation

It is square root of the arithmatic mean of the squares of speeds of various molecules of the gas at a given temperature. If `v_(1), v_(2), v_(3),...` are speeds of `n_(1), n_(2), n_(3)`.... Molecules respectively c or `u_(rms)= sqrt((n_(1)v_(1)^(2)+n_(2)n_(2)^(2)+....)/((n_(1)+n_(2)+....0)))`
RMs speed is related to T,P, V and M `:. c or u_(rms)= sqrt((3RT)/(M)) or sqrt((3PV)/(M)`