ぬく
to pull out
You get a grip on it and the whole thing comes away in your hand, cork and all. The same nuke ぬく as 抜ける, except that this time a hand did it, and the bottle is open: ぬく.
取り出す とりだす is taking a thing out of somewhere. 抜く is pulling it free of whatever was holding it.
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Emaki is not affiliated with, or endorsed by, Kaishi 1.5k or its authors. The word, reading and meaning come from the Kaishi 1.5k deck, used with their permission. The mnemonic, the note and the kanji breakdown are original work, published under CC BY-SA 4.0.