 Root was born in Iowa, receiving his bachelor's degree from Iowa State University in 1940 and master's degree from MIT in 1943, both in electrical engineering.He served as a Marine officer in World War II, in 1952 received his doctorate in mathematics from MIT, and subsequently joined Lincoln Laboratory, serving as head of its analysis group 1959–1961.From 1962 to 1987 he was Professor of Aerospace Engineering at the University of Michigan.