For gaseous state, if most probable speed is denoted by C*, average speed by C and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Most probable speed=C* = √(2RT/M)
Average speed = C = √(8RT/πM)
Mean square speed = C = √(3RT/M)
Therefore, the ratio is:
C* : C : C = √(2RT/M) : √(8RT/πM) : √(3RT/M)
Dividing by √(2RT/M)
C* : C : C = 1 : √(4/π) : √(3/2)
C* : C : C = 1 : 1.128 : 1.225