Approve carries the same swallowed prefix as appear and accept: Latin ad, "to," flattened into the following consonant. The full form is approbare, "to assent to as good," from ad plus probare, "to test something to find whether it is good," which itself rests on probus, "honest, genuine." The doubled p is the seam. English also kept the untouched relative in probe, probable and prove, so the family is easy to see once you know to look.
It came in around 1300 through Old French aprover, and the first English meaning was the older, more literal one: to demonstrate or prove. The modern sense — to regard something as good, to sanction or endorse it — grew out of that by the late 1300s, especially in reference to what authorities and parliaments did to proposals. The shift from "test whether this is good" to "declare that it is" is the whole history of the word in miniature.
approve (v.) c. 1300, apreven , approven , "to demonstrate, prove," from Old French aprover (Modern French approuver ) "approve, agree to," from Latin approbare "to assent to as good, regard as good," from ad "to" (see ad- ) + probare "to try, test something (to find if it is good)," from probus "honest, genuine" (see prove ). The meaning was extended by late 14c. to "regard or assent to (something) as good or superior; commend; sanction, endorse, confirm formally," especially in reference to the actions of authorities, parliaments, etc. Related: Approved ; approving . also from c. 1300
approve came in through Latin, and its spelling follows that family's conventions.
How that family writes these sounds
| a consonant that sounds doubled just after a prefix | double it. The prefix assimilated to the root: ad+cept, ad+prove, in+mediate, com+lectaccept, approve, immediate, collect, suffer |
What gives it away on the page
| a doubled consonant after a short prefix | The prefix assimilated to the root: ad+cept, ad+prove, in+mediate, com+lect.accept, approve, immediate, collect, suffer |