Question

The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a:

• A. Rational number
• B. Irrational number
• C. Integer
• D. Natural number

Hint:

The product of two irrational numbers is not always irrational.

Answer 1

The Correct Option is A

\[ (3+\sqrt{6})(3-\sqrt{5}) = 3^2 - \sqrt{6} \cdot \sqrt{5}. \] \[ = 9 - \sqrt{30}. \] Since \( \sqrt{30} \) is irrational, \( 9 - \sqrt{30} \) remains irrational unless given differently.