Q: Is there any irrational and rational number?

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Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).

Any, and every, irrational number will do.

Not necessarily. 0 times any irrational number is 0 - which is rational.

When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.

No. If the rational number is not zero, then such a product is irrational.

No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.

Any number with a defined end point, including 2.14, is a rational number.

You can add any irrational number.

10.01 is a rational number

Yes. Any time you multiply a rational number by an irrational number, you get an irrational number - unless the rational number is zero.

Yes. Any irrational number can be divided by itself to produce 1, which is a rational number.