We consider that the gas enclosed in a cubical vessel of edge L with coordinate axis.

Now,if we consider that a molecule having velocity v with components along the axes as v_x , v_y and v_z .

The gas we take is isotropic, i.e there is no preferred direction of velocity of molecules in vessel.Therefore, by symmetry we take-

V²_x = v²_y =v²_z  = 1/3 (v²_x +v²_y +v²_z)

Here we take mean of the velocity components in three axes (x,y,z).

So we use 1/3