Question

If $x$ and $y$ are two rational and irrational numbers respectively then which of the following are necessarily irrational.

• A. $x+y$
• B. $x-y$
• C. $xy$
• D. All of the above

Answer 1

The correct option is D All of the above

Option $D$ is correct
Let $x=2$ and $y=\sqrt{3}$
$x+y=2+\sqrt{3}$
which is irrational
$x-y=2-\sqrt{3}$
which is also irrational
$xy=2\sqrt{3}$
which is also irrational
All of them are irrational . So option $D$ is correct