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Question
Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.
Solution
Given: x is rational number and y is irrational number.
Yes, xy is necessarily an irrational number.
Example: Let x = 2, which is rational.
Let y = `sqrt(2)`, which is irrational.
Then, x × y = `2 xx sqrt(2) = 2sqrt(2)`, which is again irrational.
Also, consider the case when x = 0.
Then xy = 0, which is rational.
∴ Product of a rational and an irrational number is always irrational, only if the rational number is not zero.
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