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In constructing a square root spiral, which rule is followed to form each new right triangle?

Answer and explanation

Correct answer: A perpendicular segment of length 1 is drawn at an endpoint of the previous hypotenuse.

In a square root spiral, a unit perpendicular is added to the previous hypotenuse. By Pythagoras, the new hypotenuse has square

a^2+1

; hence successive roots are formed. A parallel segment would not ensure a right triangle. Exam tip: look for “unit perpendicular.”

Related tags

Number SystemsSquare Root SpiralPythagoras TheoremIrrational NumbersGeometryMathematicsClass 9 Mcq

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