Question

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

Answer 1

This statement is 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)`.