To explain: the sum, the difference, and the product of two rational numbers are rational numbers, whether the product of two irrational numbers necessarily irrational, to find about the sum.
are two rational numbers. Then are integers and
are integers and
Since the sum of integers is an integer, then is an integer
is a rational number
The sum of rational numbers is rational
Similarly, is an integer, so is rational, I.e., is rational
The product of rational numbers is a rational number
The sum of irrational numbers is irrational
The product of irrational numbers is not necessarily irrational.
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