Q: Can a rational number plus an irrational number equal a rational number?

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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.

Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.

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Yes

Yes, always.

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.

An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.

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

from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.

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

No. The sum of an irrational number and any other [real] number is irrational.

10+0.01 = 10.01 and it is a rational 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.

It is irrational.

The sum is a rational number.