Question

3. Let x be a rational number and y be an irrational number. Is x+y
necessarily an irrational number? Give an example in support of your
[2010, '14]
answer.
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Answer 1

Answer:

Step-by-step explanation:

No, (xy) is necessarily an irrational only when x ≠0.

Let x be a non-zero rational and y be an irrational. Then, we have to show that xy be an irrational. If possible, let xy be a rational number. Since, quotient of two non-zero rational number is a rational number.

So,(xy/x) is a rational number => y is a rational number.

But, this contradicts the fact that y is an irrational number. Thus, our supposition is wrong. Hence, xy is an irrational number. But, when x = 0, then xy = 0, a rational number.