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The sum or the difference between two Irrational Numbers could either be rational or irrational, however, it should be a real number.

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Q: What is the sum or difference of the any two irrational numbers?

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The sum of two irrational numbers may be rational, or irrational.

The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.

Can be rational or irrational.

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

No - the sum of any two rational numbers is still rational:

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.

It may be a rational or an irrational number.

It is always an irrational 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.

It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Yes.

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

Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.

No

No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.

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.

Yes

Yes, as long as the two are not mutual resiprocals.

The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.

Such a sum is always irrational.

Such a sum is always rational.

You cannot. The sum and difference cannot be the same for any pair of non-zero numbers.

sqrt(2) + sqrt(3) is irrational.

They are always rational.

1 + sqrt(2) is irrational 1 - sqrt(2) is irrational. Their sum is 2 = 2/1 which is rational.