\(( \sqrt{1375} + \sqrt{1125} ) ( \sqrt{1125} - \sqrt{1375} )\) is a ______ number.

Given:

\(\left( \sqrt{1375} + \sqrt{1125} \right) \left( \sqrt{1125} - \sqrt{1375} \right) \)

Formula used:

(a + b)(a - b) = a² - b²

Calculations:

\(\left( \sqrt{1375} + \sqrt{1125} \right) \left( \sqrt{1125} - \sqrt{1375} \right) \)

\( \sqrt{1375}^2 - \sqrt{1125}^2\)

⇒ 1375 - 1125

⇒ 250

∴ The result is a rational number. The correct answer is option (3).