Kinetic Theory of Ideal Gas

Through isotropy, we can say it enables equal distribution of velocity components in all directions. This allows us to replace directional velocity terms with a fraction of the total velocity squared. That basically simplifies the pressure formula to involve only rms speed.

This is because pressure is a result of how momentum transfers during collisions. We also know that momentum depends on velocity. The derivation shows that pressure is proportional to the average of squared velocities. That we know from the root-mean-square (rms) speed.