Explanation:

Let’s break it down:

- Option 1: 91. Not a perfect square. It’s 7 x 13, just two primes multiplied.

- Option 2: 196. That’s 14 squared. So, this is a perfect square.

- Option 3: 169. This is 13 squared—again, a perfect square.

- Option 4: 126. Not a perfect square. Prime factors? 2 x 3 x 3 x 7.

Here’s what jumps out: except for 91, the other three (196, 169, and 126) are all either perfect squares or have multiple factors, but 91 is the only one that stands out as a non-square with unique factors.

But if we focus on perfect squares specifically, then 91 and 126 are not perfect squares, while 196 and 169 are. So, really, 126 is the only one not close to any perfect square and not lying near a square number either.

Option:4, 126 is the odd one.