Mia says that anytime there is a radical in an addition expression, it automatically has an irrational number as the sum. Is she correct

Mia's statement is not correct. While it's true that the sum of irrational numbers can sometimes be irrational, there are specific cases where the sum of a radical (irrational number) and a rational number can result in a rational number.

For example, consider the radical \(\sqrt{2}\), which is an irrational number. If we add it to another \(-\sqrt{2}\) (also an irrational number), the sum is:

\[
\sqrt{2} + (-\sqrt{2}) = 0
\]

In this case, the sum is a rational number (0).

Furthermore, if you take the expression \(\sqrt{2} + 1\) (where 1 is rational), the result \(\sqrt{2} + 1\) remains irrational.

So, the presence of a radical in an addition expression does not automatically mean the result will always be irrational; it depends on the specific numbers involved.