# Does the set of irrational numbers form a group?

##### 1 Answer

No - Irrational numbers are not closed under addition or multiplication.

#### Explanation:

The set of irrational numbers does not form a group under addition or multiplication, since the sum or product of two irrational numbers can be a rational number and therefore not part of the set of irrational numbers.

About the simplest examples might be:

#sqrt(2) + (-sqrt(2)) = 0#

#sqrt(2)*sqrt(2) = 2#

**Footnote**

Some interesting sets of numbers that include irrational numbers are closed under addition, subtraction, multiplication and division by non-zero numbers.

For example, the set of numbers of the form

If you try the same with cube roots, you find that you need to consider numbers like:

More generally, if *field*.