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.
Given: x is rational number and y is irrational number.
Yes, x + y is necessarily an irrational number.
Example: Let x = 2, which is rational.
Let y = √2, which is irrational.
Then, x + y = 2 + √2, which is irrational.
∴ Sum of a rational and an irrational number is always irrational.