Answer
Since any rational number can be expressed as a fraction, and when 2 fractions are added, subtracted, or multiplied to each other, the result is always a fraction or a whole number, both of which are rational, the result will always be a rational number.
The product of 2 irrational numbers can be rational, and the sum of 2 irrational numbers can also be rational.
Work Step by Step
The product of 2 irrational numbers is not always irrational because a non-perfect integer radical (for example, $\sqrt 2$) multiplied by itself will be rational. The sum of 2 irrational numbers is also not always irrational, because there could be a number like $3+\sqrt 5$that contains an integer and a radical. If this number is added to $ -\sqrt 5$, the result would be an integer, which is rational.
