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Before making √50 in a square root spiral, which hypotenuse is formed?

Answer and explanation

Correct answer: √49

A square root spiral advances by one under the radical at each step. More precisely, if a right triangle has an existing hypotenuse √n and a new perpendicular side of length 1, the Pythagorean theorem gives the next hypotenuse as √(n + 1). For the target √50, the immediately preceding value must satisfy n + 1 = 50, so n = 49. Therefore the hypotenuse formed before √50 is √49, making option B correct. √48 is two steps earlier, √50 is the requested target rather than its predecessor, and √51 is one step later. Although √49 simplifies to 7, it is written as √49 here to show its position in the spiral sequence.

Related tags

Number-SystemsSquare-Root-SpiralPrevious-RootSquare Root SpiralNumber SystemsMathematicsClass 9 Mcq

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