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Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

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Q: Why does the sum of rational number and irrational numbers are always irrational?

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It is always an irrational number.

Real numbers can be rational or irrational because they both form the number line.

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.

No,, not always. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

No. If it was a rational number, then it wouldn't be an irrational number.

Whole numbers are always rational.

Absolutely not. A real number is always either rational or irrational. The two are mutually exclusive.

yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.

The product of two rational number is always rational.

No.A rational times an irrational is never rational. It is always irrational.

No, they are complementary sets. No rational number is irrational and no irrational number is rational.Irrational means not rational.

-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.

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