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  • 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.

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Answer: [xy is not necessarily an irrational number.]

Solution.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. So it is basically a fraction with non-zero denominator.
Irrational numbers are real numbers which cannot be represented as simple fractions.
Given that x and y be rational and irrational number respectively.
Let x = 0 (a rational number) and y=\sqrt{3}be an irrational number. then,
xy=0(\sqrt{3})=0, which is not an irrational number.
Hence, xy is not necessarily an irrational number.

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