Making squares smaller

Level pending

Given a square, is it possible to construct a square with half the area?

All terminology in this question is explained in the first note of my straightedge and compass set. More straightedge and compass construction questions can be found there.

Yes, because 1/2 is constructible Yes, because 2 \sqrt{2} is constructible This is an unsolved problem No, because 2 \sqrt{2} is not constructible

Wen Z by Wen Z , 20, Australia

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