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 necessarily correct. While it's true that the presence of a radical (like the square root of a non-perfect square) can lead to irrational numbers, it does not automatically mean that an entire expression involving radicals in an addition will always result in an irrational number.

For example, consider the expression \(\sqrt{2} + (2 - \sqrt{2})\). Here, \(\sqrt{2}\) is irrational, but \(2 - \sqrt{2}\) is also irrational. However, when you add these two numbers together, the result is:

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

which is a rational number.

Therefore, the sum of two terms involving radicals can be rational or irrational depending on the specific numbers involved in the expression.