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Yes.

Q: Is a rational number plus a rational number always a rational number?

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If both numbers are rational then x plus y is a rational number

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.

Related questions

Yes, the sum is always rational.

Yes, always.

Yes. In fact, a rational plus or minus an irrational will always be irrational.

No. A rational plus an irrational is always an irrational.

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.

If both numbers are rational then x plus y is a rational number

A natural number is always a rational number .

As much as, in these days of uncertainty, anything can be anything. As long as the constraints of a rational number are kept to, a rational number will always remain a rational number.

No.A rational times an irrational is never rational. It is always irrational.

No, never.

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

The product of an irrational number and a rational number, both nonzero, is always irrational