Question

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

Answer 1

Mia's statement is not correct. The presence of a radical in an addition expression does not automatically mean that the sum is an irrational number.

To understand this better, consider the following example:

1. If you add \(\sqrt{2}\) (an irrational number) and \(-\sqrt{2}\) (also an irrational number), the sum is:
\[
\sqrt{2} + (-\sqrt{2}) = 0
\]
which is a rational number.

2. Another example is adding \(\sqrt{4}\) (which equals 2, a rational number) to any other rational number. For instance:
\[
\sqrt{4} + 1 = 2 + 1 = 3
\]
which is also rational.

In general, the sum of two irrational numbers can be either rational or irrational, depending on the specific numbers. Thus, it's important to evaluate the specific terms in the expression rather than making a blanket statement about the presence of a radical.