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No.

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

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Q: Is an irrational number plus an irrational number rational?

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Yes

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.

10+0.01 = 10.01 and it is a rational number

It is a rational number.

It is a rational number

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

Yes

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.

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

Yes, always.

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.

10.01 is a rational number

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.

The sum is a rational number.

It is a rational number.

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