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Yes Yes, the sum of two Irrational Numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.

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Q: Can you add two irrational numbers to get a rational number?
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Related questions

If you add two irrational numbers do you get an irrational number?

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


Can you add three irrational numbers and get a rational number?

no


If three irrational numbers added together is the result irrational number?

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.


Can you add a rational number and an irrational number and get a rational number?

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.


Can 2 irrational add to an irrational number?

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


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

no


Can you add two rational numbers and get an irrational number?

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


Can you add an irrational number and a rational number to give an irrational?

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


Is it true that if you add two irrational numbers you will always get a rational number?

yes


Can you add irrational number and a rational to get a rational number?

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


What do you call the numbers that we add?

Rational and Irrational Numbers


What number do you get when you add an irrational and a rational number?

An irrational number.