Mathematical sophisms are among my favourite kind of puzzles. A sophism is not just a puzzle, it is also a beautiful work of mathematical magic, where a false claim is disguised in a seemingly correct explanation. Finding the bug in a sophism nearly always teaches you something new.
I've been collecting sophisms for as long as I know myself, yet never found the opportunity to post the collection anywhere. Let me try doing it here, one at a time. I'll start with a simple classic:
Start with a valid equality:
2 dollars = 200 centsNow square both sides to obtain:
4 dollars = 40000 centsNeed even more cents in your dollars? Just square both sides again!
Please, avoid posting direct spoilers in the comments. Indirect hints are OK.