Figuring out, realising: verb + ra (nhận ra, nghĩ ra, tìm ra)
realise, come up with, find out
Pattern: nhận / nghĩ / tìm / nhớ + ra (+ [object]) · không + [verb] + ra · [verb] + không ra (Saigon)
After verbs of thinking and searching, ra means the answer comes out: something you couldn't see or remember is suddenly clear. Nhận ra is "recognise" or "realise", nghĩ ra "think of, come up with", nhớ ra "remember (it's come back to me)", tìm ra "find out, discover", hiểu ra "finally understand". What you found comes after ra: Bác sĩ chưa tìm ra nguyên nhân. The doctors haven't found the cause yet.
For "can't", put không before the verb: không nhận ra, didn't recognise. In Saigon, không often goes between the two instead, as it does with được: Em nhớ không ra. I can't remember. Nghĩ không ra, I can't think of it.
This ra isn't movement. Chạy ra is "run out", but nghĩ ra goes nowhere: the idea comes out.
Compare the other "find" words. Tìm thấy is the usual word for finding a thing you were looking for, like your keys. Tìm ra is mostly for working out an answer, a cause or a way. Tìm được is managing to get something, like a job.
Examples
Highlighted words are what Saigon and Hà Nội say differently.
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Lâu quá không gặp, em còn nhận ra chị không?
It's been so long. Do you still recognise me?
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Em nghĩ ra một cách rồi!
I've thought of a way!
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Saigon
Ông đó tên gì ta, em nhớ không ra.
Hà Nội
Ông ấy tên gì nhỉ, em không nhớ ra.
What's his name again? I can't remember.
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Bác sĩ chưa tìm ra nguyên nhân.
The doctors haven't found the cause yet.