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Pythagoras Theorem

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIn a square root spiral, if the distance from the origin at a stage is \(\sqrt{n}\), which construction correctly produces the next point?Class 9Number SystemsSquare root spiralHard MathematicsWhile constructing a square root spiral, Reema drew a 1-unit line parallel to the hypotenuse of the previous triangle to form the next triangle. What is the main error in her construction?Class 9Number SystemsSquare root spiralHard MathematicsA student has constructed a square root spiral up to \(\sqrt{12}\). To obtain \(\sqrt{13}\), she draws a perpendicular of length 1 unit at the end of the last radius. Which conclusion is correct?Class 9Number SystemsSquare root spiralHard MathematicsWhile constructing a square root spiral, Reema used a new side of √2 units to make the triangle after the point representing √7 . What is her mistake?Class 9Number SystemsSquare root spiralHard MathematicsWhich feature of the construction of a square root spiral is correct?Class 9Number SystemsSquare root spiralHard MathematicsWhich construction rule is followed to form each new right triangle in a square root spiral?Class 9Number SystemsSquare root spiralHard MathematicsA student says that in a square root spiral, the length of the next hypotenuse after \(\sqrt{14}\) will be \(\sqrt{14}+1\). Which reasoning correctly shows the error in this statement?Class 9Number SystemsSquare root spiralHard MathematicsA student says that a base of length 10 units must first be drawn to represent \(\sqrt{10}\) on the square root spiral. Which option correctly explains the student's error?Class 9Number SystemsSquare root spiralHard MathematicsIn constructing a square root spiral, each new triangle is formed by adding a side of length 1 unit perpendicular to the hypotenuse of the previous triangle. What is the hypotenuse of the new triangle?Class 9Number SystemsSquare root spiralHard MathematicsWhat is the main reason that the successive hypotenuses in a standard square root spiral have lengths \(1, \sqrt{2}, \sqrt{3}, \sqrt{4}\), and so on?Class 9Number SystemsSquare root spiralHard MathematicsIn a square root spiral, how is the line segment representing \(\sqrt{n}\) obtained, where \(n\) is a positive integer?Class 9Number SystemsSquare root spiralHard MathematicsWhile constructing a square root spiral, a student drew a perpendicular of length 1 on the segment representing \(\sqrt{17}\) and labelled the new hypotenuse as \(\sqrt{19}\). What is the error in the student's reasoning?Class 9Number SystemsSquare root spiralHard MathematicsA student has constructed a square root spiral up to \(\sqrt{7}\) and says that \(\sqrt{8}\) cannot be constructed because 8 is not a perfect square. What is the correct next step to correct the error?Class 9Number SystemsSquare root spiralMedium MathematicsWhich construction feature is used to form each new right triangle in a square root spiral?Class 9Number SystemsSquare root spiralMedium MathematicsWhich construction is used to form the next right-angled triangle in a square root spiral?Class 9Number SystemsSquare root spiralMedium MathematicsA student says that \(\sqrt{13}\) cannot be represented on a square root spiral because 13 is not a perfect square. Which construction correctly disproves the student’s claim?Class 9Number SystemsSquare root spiralMedium MathematicsWhich number is represented by the hypotenuse of the first right-angled triangle in a standard square root spiral?Class 9Number SystemsSquare root spiralMedium MathematicsIn a square root spiral, which right-angled triangle is constructed to represent \(\sqrt{10}\)?Class 9Number SystemsSquare root spiralMedium MathematicsIn a square root spiral made of successive right triangles with unit sides, how is the point representing \(\sqrt{n}\) correctly identified?Class 9Number SystemsSquare root spiralMedium MathematicsWhile constructing a square root spiral, at what angle is the next side of length 1 unit drawn at the outer end of the previous hypotenuse to the previous hypotenuse?Class 9Number SystemsSquare root spiralMedium