To officially agree to or accept something as satisfactory; to give formal consent or permission.
From Latin 'approbare' meaning 'to make good, prove', from 'ad-' (to) + 'probare' (to test, prove good). The sense evolved from 'proving something good' to 'accepting it as good'.
Interestingly, 'approve' and 'improve' share the same Latin root 'probare' - both involve making something better or acknowledging its goodness, just from different perspectives!
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