Let $x$ be rational and $y$ be irrational. Is xy necessarily irrational? Justify your answer by an example.
Let $x$ be rational and $y$ be irrational. Is xy necessarily irrational? Justify your answer by an example.
Let $x =0$ (a rational number) and $y=\sqrt{3}$ be an irrational number.
Then, $x y=0(\sqrt{3})=0,$ which is not an irrational number.
Hence, $xy$ is not necessarily an irrational number.
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