I have been struggling to remember how first I came up with a construction for the puzzle: "**Square root**** **Draw a line x cms long. Now using ruler and compass only construct a line whose length is the square root of x." The original idea came from considering the ladder puzzle. However the construction below relies only on the application of Pythagoras' Theorem as you may be able to see from my brief hand written explanation below (where, I have just noticed, I have used y for the length of the line instead of x as quoted in the puzzle!)

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