'medically-approved' originates from the combination of 'medical' and 'approved', where 'medical' is derived from Latin 'medicus' meaning 'physician' and 'approved' from Latin 'approbare' meaning 'to approve'.

'medically-approved' evolved from the combination of 'medical' and 'approved', which were used separately in Middle English and later combined in modern English to form a compound adjective.

Initially, 'medical' referred to anything related to medicine, and 'approved' meant officially accepted. Together, they now specifically refer to medical endorsements.