Explanation:

- The square root of a number is rational if the number is a perfect square (or can be expressed as a fraction of perfect squares).

- Option 1: 2361.96

- This can be expressed exactly as \( 48.6^2 \).

- Hence, it has a rational square root.

- Option 2: 2758.28

- This number does not resolve easily into a perfect square form.

- It does not have a rational square root.

- Option 3: 72568.4

- This number similarly isn’t a perfect square.

- Its square root is not rational.

- Option 4: 62504.9

- This also isn’t a perfect square.

- The square root is irrational.

Answer: Option 1 - 2361.96