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Class 9MathematicsNumber SystemsSquare root spiralEasy
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Why is each new 1-unit line segment drawn perpendicular to the previous hypotenuse in a square root spiral?

Answer and explanation

Correct answer: To form a right triangle so that the next hypotenuse represents the square root of the next natural number

Adding a perpendicular 1-unit side forms a right triangle. By Pythagoras, the square of the new hypotenuse equals the previous square plus 1, producing successive square roots. Exam tip: identify the perpendicular unit side first.

Related tags

Number SystemsSquare Root SpiralPythagoras TheoremRight TrianglesIrrational NumbersMathematicsClass 9 Mcq
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10 more MCQs
  1. 1In a square root spiral, which segment is drawn at the end of the previous hypotenuse to form a new right triangle?
  2. 2In a square root spiral, what is the hypotenuse of the first right triangle made with base (1) unit and perpendicular (1) unit?
  3. 3If a perpendicular of length 1 unit is drawn at the end of a hypotenuse of length √2, what will be the length of the next hypotenuse?
  4. 4In a square root spiral, after the hypotenuse (\sqrt{3}), which length is obtained by adding a (1) unit perpendicular?
  5. 5Each new triangle in a square root spiral is of which type?
  6. 6In a square root spiral, how long is the new perpendicular side usually kept in each new triangle?
  7. 7Which theorem is mainly used to find the hypotenuse in a square root spiral?
  8. 8Starting from (\sqrt{1}) in a square root spiral, which is the third hypotenuse?
  9. 9In a square root spiral, the line segment representing \(\sqrt{7}\) lies between which two consecutive whole numbers?
  10. 10A square root spiral helps to represent what kind of numbers on the number line?
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