How many natural numbers lie between two consecutive squares
Answers
If you want to recall what are perfect square numbers then please refer to my article on What are the perfect square numbers. This article asks a question that how many natural numbers lie between two consecutive perfect square numbers. You can also ask the same question as how many non-perfect square numbers lie between two consecutive perfect square numbers? Can we come up with a general formula for that?
Lets write some perfect square numbers.
12=1
22=4
32=9
42=16
52=25
62=36
There are 2n natural numbers lying between two consecutive perfect square numbers n2 and (n+1)2. We can see bunch of examples.
Lets choose two consecutive perfect square numbers. Lets say that we have chosen 12 and 22. We can see that there are two numbers (2 and 3) which lie between 12=1 and 22=4. Note that 2n=2×1=2.
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