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

AI Thread Summary
The discussion focuses on finding the integers that satisfy the inequality {√n - √(23×24)}² < 1. One participant solved the problem using trial and error and seeks a systematic, step-by-step solution. It is noted that the square root of 23×24 can be approximated by the square root of 23 squared for simplicity. The conversation emphasizes the importance of sharing methods to find the solution effectively. Ultimately, the goal is to determine the specific integers that meet the given condition.
pratikaman
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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.
 
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pratikaman said:
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.
 
Notice that the square root of 23x24 is approximately the square root of 23 squared. Since asked about only integers, this approximation suffices
 

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