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It would be called a cash-out mortgage. Rates might be higher on a cash-out.
Consult your loan officer for all of the rules and how this would affect your pre-approval.
FHA has some sort of 90 day rule, where the property can only have one owner in the last 90 days. (I'm sure someone else could clairify that better)
It kept me from doing what you are saying. So if you need FHA- keep that in mind.
You know I have never heard of a cash-out FHA original loan. Cash-out FHA refis are common, but have a lot of restrictions.
I would contact the FHA or contact a lender.