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

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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. The sum of an irrational number and any other [real] number is irrational.

10+0.01 = 10.01 and it is a rational 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.

rational. if it can be expressed as a fraction, it is rational.

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No, never.

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.

The sum is a rational number.

It is irrational.

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