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to grow senile; to be childish with age
to be mentally slow; to be befuddled
to play stupid; to say something stupid (oft. on purpose; esp. as part of a comedic routine)
「呆ける」 has another reading with different meanings.
祖母は最近少し呆けてきたようで心配だ。
I am worried because my grandmother seems to have become a bit senile lately.
呆けた振りをして質問をはぐらかした。
He played dumb and deflected the question.
年を取って呆けないように毎日読書をしている。
I read every day to keep my mind sharp as I age.