Question

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

Answer 1

Yes, if x and y are rational and irrational numbers, respectively, then x + y is an irrational number.

For example,

Let x = 5 and y = `sqrt(2)`.

Then, x + y = `5 + sqrt(2)` = 5 + 1.414... = 6.414...

Here, 6.414 is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, x + y is an irrational number.