When I was at primary school I used to be fascinated by the concept of a square root... it was an interesting concept, not that I could really see any use for it. Of course, I now understand that there are many uses of it in Engineering and Computing.
By the time I got to University it was getting silly.... where the square roots of negative numbers (imaginatively called 'imaginary numbers') were crucial to the calculations of a large number of applications, such as jet engines and rocket power. To have the same number, multiplied by itself to result in a negative number made no sense, and the more I questioned it the more I was told "it doesn't matter, as we use it to cancel out another imaginary number later on". I found this explanation less than satisfactory.
Anyway, I could bang on about them all day, when all everyone wants is a cache.