Real numbers
Grade Class 10
Question:
<p><strong>Assertion (A):</strong> <span class="math-tex">\(\sqrt2\)</span>(5 - <span class="math-tex">\(\sqrt2\)</span>) is an irrational number.<br />
<strong>Reason (R):</strong> Product of two irrational numbers is always irrational.</p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: Irrational numbers do not satisfy the closure property under multiplication, meaning their product can be either rational or irrational.
<p>A is true but R is false.</p>
Correct Answer: C