Dear Mr.A.P. MASILAMANI,
We have to find out the root in natural way. Words evolved in natural way by men but keeping their regularity by considering the other similar words before forming the new word.
Finding out rationality in roots must be based on that.
We need not be a great tamil scholar but some logical reasoning in finding out the similarities of words under same roots is enough to determine the result.
'Cheer' is the root word I 've selected based on its meaning and usage in comparative with other similar words.
Take another example, 'karpu' for lady's virginity/loyalty to her husband.
Normally tamil pandits take Kal+pu. Kal here means stone. 'Rock like behaviour' and so 'karpu' is the explanation from them.
I think there is no rationality in this and it seems to be inappropriate and artificial though our grammar allows 'kal' as root.
Instead if we take 'karu-karpam-karpam-karpu' it is associated with lady molestation based on the pregnancy.
In that way if we find out root words it will be suitable than any other thing.
f.s.gandhi