SOLUTION: What is the age of this monuments if the age of monument is over 50 years old ? it's exact age is the square number of 2 years ago and will be a cube number of 2 years hence.

Question 935243: What is the age of this monuments if the age of monument is over 50 years old ? it's exact age is the square number of 2 years ago and will be a cube number of 2 years hence.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The age of the monument is a number greater than 50.
very old monuments, like the pyramids and Stonehenge are believed to be less than 5300 years old.
In 2 years the age of the monument will be a perfect cube greater than ,
and 4 less than that number (the age 2 years ago) is a perfect square.
We can calculate cubes that are greater than 52, but less than 5500,
and could be the age of the monument 2 years from now.
(It is easy with a calculator, and not that bad without one).
Then, we can check if 4 less than each cube is a perfect square.
(I know that numbers that are perfect squares must end in 0, 1, 4, 5, 6, or 9,
and that will make it easy to detect numbers that are not squares,
even without a calculator. For those not eliminated, I can try factoring).

Numbers over 50 that are perfect cubes are:
--> is not a square.
--> is a perfect square.
If the monument will be 125 years old in 2 years,
then it is years old right now.

I checked to see if there were any other plausible solutions. There were none.
The next 13 cubes are listed below, and each one is eliminated easily enough, even without using a calculator.
--> is not a square (wrong end digit).
--> is not a square, because is not a square.
--> is not a square (wrong end digit).
--> is not a square, because is not a square.
--> is not a square, because is a factor, but is not.
--> is not a square (wrong end digit).
--> is not a square, because it is greater than , and less than the closest square ending in , .
--> is not a square (wrong end digit).
--> is not a square, because is a factor, but is not.
--> is not a square. It is between and , and ends in , so it could only be or . It is neither, because , and would be a multiple of , while is not a multiple of .
--> is not a square (wrong end digit).
--> is not a square, because it is greater than , but it is less than .
--> is not a square (wrong end digit, and too large a number).
RELATED QUESTIONS
Wark�s (W) age equals Peter�s (P) age plus the cube root of Ian�s (I) age. P�s age equals (answered by ankor@dixie-net.com)

Lucas is twice as old as Emily . The product of their age is 50. Use an equation to... (answered by ikleyn)

Lauren's age is 11 years more than four times Robert's age. If the difference of the... (answered by partha_ban)

If the age of the brother is 2 years and the age of his sister is the Half of the... (answered by josmiceli)

Mike age is two third of jake’s age. If the sum of their age is thirty years, how old... (answered by ankor@dixie-net.com,greenestamps)

Matthew is y years old. His wife Jess is 2 years older. The total age of both... (answered by Theo)

The ratio of Gene's age to Sherry's age is 5: 8. Five years later, the ratio of Gina's... (answered by josgarithmetic)

Three years ago, my age was a prime number. � This year, my age is a multiple of 4. (answered by Edwin McCravy)

Please help me with this...TIA Joey's age is five years less than Cora's age. The sum... (answered by ikleyn)