What word "request" or "ask" is more appropriate if we are talking about formal letter?
- I am writing to request few days off.
- I am writing to ask about few days off.
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You don't really say why you are asking. If you are making a formal request for time off, then:
I am writing to request a few days off.
But if you are asking if taking time off is possible, then:
I am writing to ask about the possibility of taking a few days off.
I am writing to ask about taking a few days off.