Question 257611: Augustus de Morgan wrote in 1864, "At some point in my life, the square of my age was the same as the year." When was he born?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he would have to have been 43 in 1849.
since he wrote this in 1864, then he could have lived in the late 1700's to the early 1900's.
42 squared = 1764 which would have made him 42 years old in 1764 which would mean that he would have been 142 years old in 1864 which is impossible so it couldn't be 42 squared.
44 squared = 1936 which would have made him be born in 1892 which is also impossible.
43 squared in 1849 is possible, so that has to be the answer.
I narrowed the possible solution down by taking the square root of 1800 and the square root of 1900 to get:
square root of 1800 = 42.426....
square root of 1900 = 43.588....
this narrowed down the possible age to between 42 and 44.
then it was simply a matter of solving for:
42 squared = 1764
43 squared = 1849
44 squared = 1936
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