Question

How many numbers lie between squares of the following numbers? 

1. \(12\) and \(13\) 
2.  \(25\) and \(26\) 
3.  \(99\) and \(100\)

Answer 1

We know that there will be \(2n\) numbers in between the squares of the numbers \(n\) and \((n + 1)\).
(i) Between \(12^2\) and \(13^2\), there will be \(2 \times 12 = 24\) numbers

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(ii) Between \(25^2\) and \(26^2\), there will be \(2 \times 25\) = \(50\) numbers

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(iii) Between \(99^2\) and \(100^2\), there will be \(2 \times 99\) = \(198\) numbers