How many natural numbers lie between squares of the following natural numbers? (I)12 and 13        (ii)  25 and 26         (iii)  99 and 100

Explanation

To find how many natural numbers lie between the squares of the given natural numbers, we can use the formula that states the number of non-perfect square natural numbers between \( n^2 \) and \( (n+1)^2 \) is equal to \( 2n \).

Let's solve each part step by step.

### Part (I): Between the squares of 12 and 13

1. **Identify \( n \)**: Here, \( n = 12 \).
2. **Apply the formula**: The number of natural numbers between \( 12^2 \) and \( 13^2 \) is given by:
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