Understanding Block Version Validation

I was checking out a recent block and noticed that the version isn't just the base version 0x00000002. Do miners throw in extraNonce too, or does that only get added in the merkle root?

Yeah, you’re right. The version is more than just 0x02. Miners add extraNonce, and it’s worked out as version plus 1 (if segwit is on) plus 2 (if extraNonce is used) plus the actual extraNonce. The merkle root gets included in the version field after some bitwise tweaks.

So, if I stick with the base version, can I still hash my way to the right one? Or do I have to mess with the merkle numbers too? I can’t seem to find any solid docs linking the merkle root and the version number.