Question:
The product of any two irrational numbers is
(a) always an irrational number
(b) always a rational number
(c) always an integer
(d) sometimes rational, sometimes irrational
Solution:
(d) We know that, the product of any two irrational numbers is sometimes rational and sometimes irrational.
e.g., $\sqrt{2} \times \sqrt{2}=2$ (rational) and $\sqrt{2} \times \sqrt{3}=\sqrt{6}$ (irrational)
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