Using concepts from the Kinetic Molecular Theory, the pressure of a gas is defined as
P = nM<v2>/V, where n = number of moles, M = molar mass, <v2> = mean of the square of speeds
In three-dimensions, since gas molecules are moving randomly, vrms is defined as vrms = (3<v2>)1/2. From this, derive the formula for the root-mean-square speed of an ideal gas.