The construction of a square root spiral starts with which basic length?

Correct answer: (1) unit

The direct answer is A, a 1-unit length. A square root spiral, also called the spiral of Theodorus, begins with a right triangle whose two perpendicular sides are 1 unit each. By Pythagoras, its hypotenuse is (\sqrt{1^2+1^2}=\sqrt{2}). Then a new 1-unit perpendicular is drawn at the end of the previous hypotenuse, producing the next right triangle and (\sqrt{3}), and the process continues. Option A is correct because the first basic segment has length 1 unit. Option B, 2 units, would not give the standard starting construction and would change the sequence. Option C, (\sqrt{2}), is the first hypotenuse obtained after starting with unit sides, not the original basic length. Option D, (\sqrt{3}), is reached later after another triangle, so it cannot be the starting length. The exact idea is that each new triangle has one side of 1 unit and the earlier hypotenuse as the other side. Memory cue: start with 1, then the hypotenuses become (\sqrt{2}), (\sqrt{3}), (\sqrt{4}) and so on.