The
meaning of approve changes when you add the preposition of
to make approve of. Approve'by itself means 'sanction' or 'endorse'
as in these two examples. In the first, an accountant is speaking
and in the second, a university admissions tutor.
'I cannot approve the reimbursement because you haven't given me the
receipts for your expenditure.'
'I cannot approve your application to study law because you do not
have the relevant qualifications.'
If
you approve of something, then you consider it to be good or
you agree with it. Consider:
'I don't approve of smoking in restaurants because it
is so upsetting usually for non-smokers.'
'Why don't you approve of my friends? They are all good
upright people.'