Question:
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a:
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a:
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The product of two irrational numbers is not always irrational.
Updated On: Oct 27, 2025
- Rational number
- Irrational number
- Integer
- Natural number
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The Correct Option is A
Solution and Explanation
\[
(3+\sqrt{6})(3-\sqrt{5}) = 3^2 - \sqrt{6} \cdot \sqrt{5}.
\]
\[
= 9 - \sqrt{30}.
\]
Since \( \sqrt{30} \) is irrational, \( 9 - \sqrt{30} \) remains irrational unless given differently.
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