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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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The difference of two irrational numbers is an irrattinal number?
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.
The sum of two irrational is always irrational?
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.
Is the sum of two irrational numbers necessarily irrational?
Yes, as long as the two are not mutual resiprocals.
Is there a rational number between any two irrational numbers?
Yes. To find it, evaluate both irrationals until the numbers show a difference in one of their later digits. Truncate the irrationals after this digit, sum them, then divide by 2. Job done.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
