Question

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

Answer 1

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

False

Reason:
However, `sqrt2` is not rational because there is no fraction, no ratio of integers that will equal `sqrt2`. It calculates to be a decimal that never repeats and never ends. The same can be said for ` sqrt3`. Also, there is no way to write `sqrt2+sqrt3` 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+sqrt3` and `1-sqrt2`. In this case, the irrational portions just happen to cancel out leaving: `1+sqrt2+1-sqrt2=2` which is a rational number (i.e. 2/1).