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No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving Irrational Numbers give you an irrational number, but there are a few exceptions.

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Q: Is the sum of two irrational number is always irrational?

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

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.

irrational

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.

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

It may be a rational or an irrational number.

not always. nothing can be generalized about the sum of two irrational number. counter example. x=(sqrt(2) + 1), y=(1 - sqrt20) then x + y = 1, rational.

Such a sum is always rational.

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

Sqrt(2) and sqrt(3)

Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)

They are always rational.

Yes

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

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.

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

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

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

No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.

Because the irrational parts may cancel out.For example, 1 + sqrt(2) and 5 - sqrt(2) are both irrational but their sum is 1 + 5 = 6.

Can be rational or irrational.

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

The sum of two odd primes is always an even answer or number.

Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.