The corrected sentence is: "Rose has sung that well-known folk song 'If I Had a Hammer' two times at the Wakefield County Folk Fair."
Changes made:
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"sang" to "sung": "Sung" is the past participle of "sing," while "sang" is the simple past form. In this context, "has sung" requires the past participle.
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Added a hyphen in "well-known": This compound adjective should be hyphenated as it functions together to modify the noun "folk song."
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Quotation marks around the song title: The title of the song "If I Had a Hammer" should be enclosed in quotation marks to indicate that it is a title.
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Capitalization of "Wakefield County Folk Fair": Proper nouns such as the name of places and events should be capitalized.
By making these adjustments, the sentence is grammatically correct and clearly communicates the intended meaning.