Do split ends go away with time?

I am in the process of growing out my hair, but I may have some slight split ends. If I were to let it continue to grow out (while trimming it every 3 months - as per standard) until it reached the length I want to keep it at, then keep trimming it when it gets too long, will I eventually trim off the split ends and replace them with healthy hair? Or do I have to cut them off at the root before my hair grows out all the way?
Do split ends go away with time?
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