Correct spelling, explanation: the word prove is a source of some confusion due to the related word: proof. Both words stem from the Latin probare, later French preove. The spelling of prove stayed with only one o, while proof has been changed in the Middle ages, likely because of the fact that it was used more.

Definition of prove:
verb
1. to showcase something is a fact
If you want to win, you have to prove that you are the best.
I can prove he was responsible for the crime; I have evidence!

Idioms with prove:
prove someone wrong – to do something to show that someone’s predictions were false
My mom had always said that if I go out too much I won’t get anywhere in life, so I decided to prove her wrong and became rich thanks to networking.
prove (something) to (someone) – to show someone you are right about something
You can trust that I do my job well, I shouldn’t have to prove it to you.

Incorrect spelling, explanation: you may be tempted to think proove is the correct spelling, but it is not, despite the fact it’s so similar to the word proof. In fact, both these words have the same Latin root word – probare, which was later adapted into French preove. Then, in Old English proof as a noun was most likely used more, which is why it was adapted more fully into English spelling, while prove stayed more similar to its French predecessor. In any way, try to remember that prove is like love and it only has one o.