Simple question, apologies. This is from some sample high school math questions, target is age 16 pupils. I don't think any great sophistication is expected.
$$ P + Q = \sqrt {5}. $$
$P$ is a rational number and $Q$ is an irrational number. Give possible values of $P$ and $Q$.
I can think of the trivial $$ P = 0, Q = \sqrt {5}. $$ I'm not even sure that the pupil would be expected to come up with $$ P = 2, Q = (\sqrt {5} - 2). $$ I don't think $Q$ could then be simplified to another named irrational. Any ideas what an expected answer might be?