Question

13. Let X be a rational number and Y be an irrational number. Is x +y necessarily an irrational ? Justify
your answer with an example.
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Answer 1

No because x can be 0 and any real number multiply by 0 the answer is always 0.

So we can say that multiplication of rational and irrational number can either be rational or irrational.

Answer 2

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Let X be a rational number and Y be an irrational number. Then x +y is NOT necessarily an irrational

For example

$2 + \sqrt{3} \: \: and \: \:2 - \sqrt{3 }$

are irrational but their sum 4 is a rational

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