Age in a square year

EasyBrainteasers~4m

The mathematician Augustus De Morgan liked to say that he was $x$ years old in the year $x^2$ . He died in $1871$ . Assuming nobody lives past $120$ years, what is $x$ ?

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Being $x$ in year $x^2$ means he was born in year $x^2-x$ .
Find a perfect square $x^2 \le 1871$ giving a lifespan under $120$ . Try $x$ in the low $40$ s.

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Asked at: Jane Street, Citadel

Age in a square year

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