'inadvertently' originates from Latin, specifically the word 'inadvertentem,' where 'in-' meant 'not' and 'advertentem' meant 'turning the mind to.' 'Approved' comes from Latin 'approbare,' where 'ad-' meant 'to' and 'probare' meant 'test or prove.'

'inadvertentem' transformed into the English word 'inadvertent,' and 'approbare' became the English word 'approve' through Old French 'aprover.'

Initially, 'inadvertent' meant 'not turning the mind to,' and 'approve' meant 'to test or prove.' Over time, 'inadvertently-approved' evolved to mean 'accidentally given approval.'