The sum of two irrational number is an irrational number (True/False).

Question:

The sum of two irrational number is an irrational number (True/False).

Solution:

The sum of two irrational numbers is an irrational number (True/False)

False

Reason:

However, $\sqrt{2}$ is not rational because there is no fraction, no ratio of integers that will equal $\sqrt{2}$. It calculates to be a decimal that never repeats and never ends. The same can be said for $\sqrt{3}$. Also, there is no way to write $\sqrt{2}+\sqrt{3}$ as a fraction. In fact, the representation is already in its simplest form.

To get two irrational numbers to add up to a rational number, you need to add irrational numbers such as $1+\sqrt{2}$ and $1-\sqrt{2}$. In this case, the irrational portions just happen to cancel out leaving: $1+\sqrt{2}+1-\sqrt{2}=2$ which is a rational number (i.e. 2/1).