After constructing (\sqrt{2}) in a square root spiral, what construction is done next?

Correct answer: Draw a (1) unit perpendicular at the end of (\sqrt{2})

The direct answer is A: draw a 1-unit perpendicular at the end of (\sqrt{2}). The construction works by making a right triangle at every stage. Start with a unit-based triangle to obtain hypotenuse (\sqrt{2}). Next, keep (\sqrt{2}) as one side and draw a perpendicular side of 1 unit. Pythagoras gives the new hypotenuse (\sqrt{(\sqrt{2})^2+1^2}=\sqrt{3}). Option A is correct because this is exactly the next construction needed. Option B, erasing the segment, destroys the construction and cannot create the next square root. Option C, making a denominator zero, is unrelated to a geometric spiral and division by zero is not permitted. Option D, converting the triangle into a square, is not the method; the next value is created by a new right triangle, not by making a square. The word “perpendicular” means meeting at a right angle of 90 degrees. Memory cue: at every new endpoint, add one unit at a right angle; the hypotenuse then moves from (\sqrt{n}) to (\sqrt{n+1}).