Why did some of the number roots (like oct-, tri-, dec- ) stay the same for both Greek and Latin?

Because the Romans saw no reason to change them....

Numbers are among the words which persist most strongly through language developments. In particular the number 'two' is present in some form of the original postulated proto-indoeuropean language in just about every language system in Eurasia.

They're both Indo-European languages. If you look up the numbers in Sanskrit, which is older than either Greek or Latin, you'll see some similarities there, too. They're all related.