TITLE: Covering one square by three smaller squares
QUESTION [10 upvotes]: Consider square of side $1.25$ can it be covered by three squares of side $1$ ? 
I think it's impossible but I'm not sure how to show it.

REPLY [3 votes]: I can't compete with David's picture, but you might find Squares Covering Squares (part of Erich's Packing Center) useful. In particular it shows that Henry Dudeney found (in 1931) a covering not unlike David's which allows three unit squares to cover a square of side length $\sqrt{\frac{1+\sqrt5}{2}}\approx1.27202$.
In particular this answers Ivo Beckers' question: the minimum side length to cover a square of side 1.25 is $\sqrt{\frac{5\sqrt5+5}{8}}\approx0.982689222,$ assuming the optimality of Dudeney's construction.