Martin Carroll, Sr.

Mary McDonough 1811-1886 https://www.findagrave.com/memorial/74282305

Children:
Martin Michael Carroll 1834-1892 https://www.findagrave.com/memorial/155206835
Ann C. Carroll Halloran 1839-1913 https://www.findagrave.com/memorial/111307226
Bridget Carroll Mulligan 1840-1915 https://www.findagrave.com/memorial/100692816
John W Carroll 1841-1895 https://www.findagrave.com/memorial/74282411
Susan Carroll
Henry Carroll
Luke Carroll
Mary Carroll

United States Census, 1880:
Name Martin Carroll
Event Place Burlington, Des Moines, Iowa, United States
Gender Male
Age 70
Marital Status Married
Race White
Occupation Laborer
Relationship to Head of Household Self
Birth Year (Estimated) 1810
Birthplace Ireland
Father's Birthplace Ireland
Mother's Birthplace Ireland
Sheet Letter B
Sheet Number 146
Person Number 0
Volume 1
Name, Role, Gender, Age, Birthplace:
Martin Carroll Self M 70 Ireland
Mary Carroll Wife F 70 Ireland
District ED 110
Sheet Number and Letter 146B
Household ID 7764387
Affiliate Name The U.S. National Archives and Records Administration (NARA)
Affiliate Publication Number T9
Affiliate Film Number 0337
GS Film Number 1254337
Digital Folder Number 005160599
Image Number 00297
Citing this Record: "United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MD2H-PGS : accessed 4 February 2016), Martin Carroll, Burlington, Des Moines, Iowa, United States; citing enumeration district ED 110, sheet 146B, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0337; FHL microfilm 1,254,337.
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The following may be him at findagrave but the linked spouse and child don't match up:
https://www.findagrave.com/memorial/102912624
It's possible it IS the right man and that someone has incorrectly linked that other spouse and child to him.

Do we KNOW the following naturalization record is this particular Martin Carroll? No, we can't know for sure, but the birth year and place match.
United States, New England Petitions for Naturalization Index, 1791-1906:
Name Martin Carroll
Event Type Naturalization
Event Date 1837
Event Place Maine
Birth Year 1810
Birthplace Waterford, Ireland
Affiliate Publication Title Index to New England Naturalization Petitions, 1791-1906
Affiliate Publication Number M1299
Affiliate Film Number 60
GS Film number 1429730
Digital Folder Number 4639176
Image Number 03775
Citing this Record: "United States, New England Petitions for Naturalization Index, 1791-1906," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:VXR3-42Z : 11 March 2018), Martin Carroll, 1837; citing Maine, NARA microfilm publication M1299 (Washington D.C.: National Archives and Records Administration, n.d.), roll 60; FHL microfilm 1,429,730.