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Q: Is the sum of a rational number and an irrational number always irrational?

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Yes.

It is always an irrational number.

Any, and every, irrational number will do.

The sum of two irrational numbers may be rational, or irrational.

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.

Related questions

It is always irrational.

Such a sum is always irrational.

It is always an irrational number.

Yes.

It is always an irrational number.

Wrong. It is always an irrational number.

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.

Yes, that is so.

The sum of a rational and irrational number must be an irrational number.

No. In fact the sum of a rational and an irrational MUST be irrational.

The value of the sum depends on the values of the rational number and the irrational number.

The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.