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It is not! All you need is a square whose sides are sqrt(32) = 4*sqrt(2) in length.

You might try and argue that 4*sqrt(2) is an irrational number and so cannot be calculated exactly so it is not possible to draw a side of length 4*sqrt(2). Faulty argument.

Draw a 4*4 square. Easy enough! The diagonal of this square has length sqrt(32) = 4*sqrt(2). So now you have a line of the required length.

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Q: Why is it impossible to cut out a 32 unit square?
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A square yard is a unit of area. A mile is a unit of distance. The two units are therefore incompatible.


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