You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.
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Question: Category: THE 19th CENTURY 
Clue: 1853 purchase that brought the contiguous U.S. about up to its present area

Answer: the gadsden purchase


Question: Category: MATH TERMS 
Clue: The term surd refers to irrational numbers like this number's square root, 1.7320508...

Answer: 3


Question: Category: HOMOPHONES 
Clue: The vertical part of a doorframe or the current fashion

Answer:
stile/style