How Many Integers Meet the Condition {√n - √(23×24)}² < 1?

[pratikaman]

How many integers satisfy {√n-√(23×24)}^2<1


I was able to solved this by trial and error method , but i want to know systematic step-wise solution.

 

[Ray Vickson]

How many integers satisfy {√n-√(23×24)}^2<1


I was able to solved this by trial and error method , but i want to know systematic step-wise solution.

Show us what you did; perhaps your method was as good as anything.

 

[AmritpalS]

Notice that the square root of 23x24 is approximately the square root of 23 squared. Since asked about only integers, this approximation suffices