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No.

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

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

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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.

Yes

10+0.01 = 10.01 and it is a rational number

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.

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

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.

Yes

No, never.

Yes, always.

No. A rational plus an irrational is always an 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.

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.

It is irrational.

The sum is a rational number.

10.01 is a rational number