The words applaud and explode have a common phoneme, but very different spellings and meanings. So are they somehow related?
Well, it turns out that they both come from the latin word plaudere (to clap), but they took different routes:
Applaud: ad (to) + plaudere (clap) became applaudere (clap) in Latin then applaudir in French, then applaud in 15th century English.
Explode: ex (to) + plaudere (clap) became explodere (drive off stage by clapping) in Latin then explode (reject scornfully, discard) in 16th century English.
Meanwhile, burst with a noise was displode in Old English.
In the 18th century, displode somehow became obsolete and explode took its meaning, which is fine as people are not driven off stage by clapping anyway!
If you already knew that, BRAVO!