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Irrational Numbers

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

MathematicsWhich inequality is correct to identify the position of \(\sqrt{125}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsIn a standard square root spiral, which group of hypotenuse labels represents points at integral distances from the origin?Class 9Number SystemsSquare root spiralLevel 19Hard 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 spiralLevel 19Hard MathematicsIn a square root spiral, how is the line segment representing \(\sqrt{n}\) obtained, where \(n\) is a positive integer?Class 9Number SystemsSquare root spiralLevel 19Hard 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 spiralLevel 19Hard 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 spiralLevel 21Medium MathematicsWhich construction is used to form the next right-angled triangle in a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium 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 spiralLevel 21Medium MathematicsWhat is the correct statement about \(\sqrt{24}\) and \(\sqrt{25}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhich number is represented by the hypotenuse of the first right-angled triangle in a standard square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, which right-angled triangle is constructed to represent \(\sqrt{10}\)?Class 9Number SystemsSquare root spiralLevel 21Medium 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 spiralLevel 21Medium MathematicsWhile constructing the next triangle after \(\sqrt{7}\) in a square root spiral, a student takes the other perpendicular side as \(\sqrt{7}\) units. Which statement correctly fixes the error?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhich side pair is correct for constructing \(\sqrt{5}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, a 1-unit perpendicular side is added to the previous hypotenuse, and the new hypotenuse represents the next square root. Which theorem is this conclusion based on?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhich statement about the type of \(\sqrt{2}\) and \(\sqrt{8}\) in a square root spiral is correct?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, what is done with the hypotenuse of the previous triangle to construct each new right triangle?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhile constructing a square root spiral, a student adds a new perpendicular side of length 1 unit to the previous hypotenuse to form each right triangle. Which statement about the hypotenuse of the next triangle is correct?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, the point representing which of the following numbers will be at an integral distance from the origin?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn the construction of a square root spiral, which feature connects each new right triangle to the preceding triangle?Class 9Number SystemsSquare root spiralLevel 21Medium