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File:Pythagorean tiling to invent square root of 5.svg

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Square root of 5 is the dimension h of the square in red dashed lines,  because its area is 5.  It is also the hypotenuse length of a right triangle of which the perpendicular edges measure 1 and 2:   h × h = 1 × 1 + 2 × 2  (Pythagorean theorem).

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