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In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two sections p and q. If we denote the length of the altitude by h, we have the relation h2 = p*q (Euklids altitutude theorem).

So, first draw the square root of 2 as the diagonal of a square with side length 1, then construct a right triangle with p=1 and q= sqrt(2) by using the Thales theorem and its altitude will be fourth root of 2 according to Euclids theorem.

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