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Q: Can you add two irrational numbers and get a rational number?

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No. The set of rational numbers is closed under addition (and multiplication).

No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.

yes

You can add any irrational number.

Do you mean can we subtract one rational number from another rational number and get an irrational number as the difference? I'm not a mathematician, but I suspect strongly the answer is no. Wouldn't this imply that we can sometimes add a rational number to an irrational one, and get a rational number as a sum? That doesn't seem possible.Ans 2.It isn't possible. Proof :-Given two rational numbers, multiply the two denominators.Express each rational in terms of the common multiple.Algebraically add the numerators of the new rational numbers.Put this over the common multiple; there's the result expressed as a ratio.

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no

no

Not necessarily. The sum of two irrational numbers can be rational or irrational.

You can not add irrational numbers. You can round off irrational numbers and then add them but in the process of rounding off the numbers, you make them rational. Then the sum becomes rational.

no

Yes. The sum of two irrational numbers can be rational, or irrational.

No, the result is always an irrational number. In more advanced math it is possible to add an infinite amount of rational numbers by way of Taylor Series and get an irrational number. This is how numbers like "Pi" and "e" are derived.

No. The set of rational numbers is closed under addition (and multiplication).

No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.

An irrational number.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

Rational and Irrational Numbers

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