Let x be a rational number and y be an irrational number.
Question:

Let x be a rational number and y be an irrational number. Is x + y necessarily an irrational number? Give a example in support of your answer.

Solution:

x be a rational number and y be an irrational number then x + y necessarily will be an irrational number.

Example: 5 is a rational number but $\sqrt{2}$ is irrational.

So, $5+\sqrt{2}$ will be an irrational number.