Etymology of 'care' and 'educate'

Hello etymology folks! I really enjoyed the discussion for my last post so Im here with another one:

I wonder if theres any etymological linkage between 'care' and 'educate'?

I had this thought because I saw that 'educate' goes back to 'educare' --- unfortunately educare seems to break down to 'e' + 'ducare' and traces to 'dewk' meaning 'to lead out', while care seems to come from 'concern', 'karo' etc..

But since it makes sense that there's some overlap between the ideas of 'care' and 'educate', Im just wondering if theres any etymological linkage between these two?