# 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.

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