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example for sum of rational numbers is 1/3 + 1/5 Example for sum of irrationals is Pi + e where e is is base of natural log Another is square root of 2 + square root of 3.

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Q: Example for sum of a rational number and irrational number?

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The sum of a rational and irrational number must be an irrational number.

Such a sum is always irrational.

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

Yes

The square root of any positive integer can only be a WHOLE NUMBER or IRRATIONAL, so the square root of 7 is irrational.On the other hand, the sum of a rational and an irrational number is always irrational.

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The sum of a rational and irrational number must be an irrational number.

No. In fact the sum of a rational and an irrational MUST be irrational.

The value of the sum depends on the values of the rational number and the irrational number.

It is always irrational.

The sum is irrational.

Such a sum is always irrational.

An irrational 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.

The sum of the three can be rational or irrational.

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.

Any, and every, irrational number will do.

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.