If x is a rational number and y is an irrational number, then

Both x + y and xy are necessarily irrational

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Both x + y and xy are necessarily rational

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xy is necessarily irrational, but x + y can be either rational or irrational

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x + y is necessarily irrational, but xy can be either rational or irrational

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Solution

The correct option is D x + y is necessarily irrational, but xy can be either rational or irrational
If $x$ is a rational number and $y$ is an irrational number then sum of $x + y$ is an irrational number.

If $x$ is a rational number and $y$ is an irrational number then $x y \Rightarrow x y$ can be rational or irrational number ,like 0 and $\sqrt{3}$

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Similar questions

State True or False.

Let

x

be rational and

y

be irrational, then

x y

necessarily irrational.

Q. Let x and y be rational and irrational numbers, respectively, then x + y necessarily an irrational number.

State True or False.

Q. Question 2
Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

Q. Question 2
Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

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 answer.

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