If you were 35 years old in the year 1225. It would be a very special time mathematically because 35^2 = 1225. That is the square of your age at the moment is equal to the year. Augustus de Morgan, a famous mathematician was one of those lucky people and in 1864 he wrote ''At some point, in my life the square of my age was the same as the year.'' When was Augustus de Morgan born?

Ares/Alfredo/Liahh/John/Ariel -- please use the same name for your posts.

please help me.

Assume the square occurs when he is in his 40's.

To find out when Augustus de Morgan was born, we need to solve the equation where the square of his age is equal to the year he was born. Let's call his birth year "B".

The equation based on the information provided is:
(age)^2 = B

To solve this equation, we can take the square root of both sides:
sqrt((age)^2) = sqrt(B)

Simplifying this, we get:
age = sqrt(B)

According to the information given, in the year 1864, de Morgan wrote "At some point, in my life the square of my age was the same as the year." This means that in 1864, the square of his age would be equal to 1864.

Let's substitute this into our equation:
age^2 = 1864

Taking the square root of both sides:
sqrt((age)^2) = sqrt(1864)
age = sqrt(1864)

Now we need to look for a perfect square less than or equal to 1864. To do this, we'll find the square roots of numbers starting from 1 and going up until we find a perfect square that is less than or equal to 1864.

sqrt(1) = 1
sqrt(4) = 2
sqrt(9) = 3
sqrt(16) = 4
.
.
.
sqrt(1764) = 42 (since 42^2 = 1764)
sqrt(1824) = 42.7228
sqrt(1864) = 43.1317

From the calculation, we find that the largest perfect square less than or equal to 1864 is 1764, which is equal to (42)^2.

Therefore, we can say that Augustus de Morgan was born in the year 1764.