The sum of two irrational number is an irrational number (True/False).
The sum of two irrational numbers is an irrational number (True/False)
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).
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- Euclid’s Division Lemma