Express each of the following as the sum of two consecutive natural numbers : (I)`21^2` (ii) `13^2` (iii) `19^2`

Explanation

To express each of the given squares as the sum of two consecutive natural numbers, we will follow a systematic approach. We will use the formula for two consecutive natural numbers based on the square of a number \( n \):

1. The two consecutive natural numbers can be expressed as:
- \( p = \frac{n^2 - 1}{2} \)
- \( q = \frac{n^2 + 1}{2} \)

2. The sum of these two numbers will equal \( n^2 \):
- \( p + q = n^2 \)
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