Explanation:

- Let's break down the relationships:

- The first pair is 27 : 196. \(27\) is \(3^3\) and \(196\) is \(14^2\).

- The second pair is 19 : 100. \(19\) doesn't directly relate but \(100\) is \(10^2\). The logic isn't purely arithmetic.

- Now, the third pair is 17 : ?

- We need to find a number whose square maintains a consistent logic with the given pairs.

- Looking at possible patterns:

- The outputs, 14 and 10, are just integers formed by mathematical derivations from the inputs, like squares.

- We need another square:

- Option 1: \(57\) (not a clear logic)

- Option 2: \(81\), which is \(9^2\) (seems more consistent as a pattern)

- Option 3: \(89\) (random structure)

- Option 4: \(96\) (random structure)

- Based on the analysis, Option 2: 81 is the correct answer.

- Since 9 squared is 81, it fits intelligently with other squared integers.

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