Radical of Year of Birth

Stella’s grandfather was born during the 19th century. The square root of the year he was born, plus the square root of the year that Stella’s cousin Elspeth was born, equals the age of Stella’s grandfather when he died. So in what year did her gramps die, how old was he at his death, and how old is Elspeth now?

Show/Hide Solution

412 = 1681
422 = 1764
432 = 1849
442 = 1936
452 = 2025
We need some perfect squares in the 19th and 20th centuries.
So gramps must have been born in 1849, and Elspeth must have been born in 1936. Those square roots are 43 and 44, so gramps died at age 87.

Then 1849 + 87 = 1936, the year he died.
Elspeth turns 2014 – 1936 = 78 this year.

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