Irrational and Rational Numbers General Question

(Prepswift question included)
Hi,

I don’t know if I’m doing this right so bear with me please. I’m working on the Arithmetic Progress Quiz #9. I noticed that there are a lot of questions about adding/multiplying rational and irrational numbers together in different combinations, and whether or not the result is itself an irrational/rational number.

See below for an example:

I didn’t see this topic covered in any of the videos, to my knowledge. I understand the concept, but I’m just curious how familiar we should be with these rules? For example, should I memorize that adding an irrational number to a rational number will always result in an irrational number?

Thanks!

There’s no reason to memorize anything, but it might be useful to intuitively understand why that’s the case.

2 Likes

Awesome, thank you