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Why does the sum of rational number and irrational numbers are always irrational?
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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The sum of rational numbers and an irrational number?
It is always an irrational number.
Is a real number always irrational?
Real numbers can be rational or irrational because they both form the number line.
What is an irrational plus two rational numbers?
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.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Are rational numbers is an irrational numbers?
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.
