I did exactly the same thing when teaching physics in college for many years. I made the numbers easy, but made people memorize formulas. No calculators or "cheat sheets" allowed, but you could leave an answer as pi/sqrt(2).

I would tell the students: "The numbers should come out easy. If you get something weird, then one of us made a mistake!"

This simple change made a huge improvement in comprehension in the class. It wasn't about "number jamming" any more, but about learning.

"finding a square root on paper."

That's painful!

Actually it's pretty easy. It also follows from the basics of long division, which underpins how CRC algorithms work.