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See if the square root of starting number is say 5.6 and ending number is lets say 8.1 then in between you have 5.7 ,5.8, 5.9, 6, 6.1 and so on till 8.1. But we know that square root of only perfect square will be an integer, so the number of integers between 8.1 and 5.6 will tell us exactly how many perfect squares are there between corresponding numbers.
Sherlock and Squares
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See if the square root of starting number is say 5.6 and ending number is lets say 8.1 then in between you have 5.7 ,5.8, 5.9, 6, 6.1 and so on till 8.1. But we know that square root of only perfect square will be an integer, so the number of integers between 8.1 and 5.6 will tell us exactly how many perfect squares are there between corresponding numbers.