To See Through
To Get To The Bottom Of
transitive verb, ichidan verb
極める is "to carry to extremes." If you carry something to the extremes (aka the end), and then you see it to the extremes while doing it, you're going to see through whatever you're doing.
みきわめる
The readings come from the words 見る and 極める put together. See through this word and learn it.
自分のこの目で真実を見極めたいんです。
I want to see the truth with my own eyes.