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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 of the following statements is correct about the construction of a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, which of the following numbers is represented by a line segment of rational length?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, what length of new perpendicular is drawn to the previous hypotenuse to form each new right triangle?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhat is the correct number-line position of \(\sqrt{130}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhat is the correct reason for \(\sqrt{15}\) being formed from \(\sqrt{14}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, in which interval will \(\sqrt{120}\) lie on the number line?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhich statement about \(\sqrt{72}\) and \(\sqrt{81}\) in a square root spiral is correct?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsWhat is the main reason that the successive hypotenuses in a square root spiral have lengths \(\sqrt{2}, \sqrt{3}, \sqrt{4}\), and so on?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsA student constructs \(\sqrt{13}\) on a square root spiral by drawing a perpendicular segment of length 1 at the point for \(\sqrt{12}\) and joining its end to the origin. Why is this reasoning correct? What is the square of the new hypotenuse?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, in which interval will the length \(\sqrt{45}\) lie on the number line?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsA student says, “The new hypotenuses in a square root spiral represent square roots of perfect squares only.” How should this statement be judged?Class 9Number SystemsSquare root spiralLevel 21Medium MathematicsIn a square root spiral, what type of number is represented by the point for \(\sqrt{17}\)?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhich sequence is represented by the lengths of successive hypotenuses in a standard square root spiral?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhile constructing a square root spiral, between which two segments is each new right angle formed?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhile constructing a square root spiral, a student uses 2 cm instead of 1 cm as the perpendicular side of every new right triangle. Which conclusion about the figure is correct?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhile constructing a square root spiral, a student says that to obtain \(\sqrt{8}\) after \(\sqrt{7}\), a perpendicular of length 1 should be drawn to the previous hypotenuse \(\sqrt{7}\). What is the status of the student's statement?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhile locating \(\sqrt{10}\) on the number line using a square root spiral, a student says it will be to the right of 4 because 10 is greater than 4. What is the correct correction to this error?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsIf after constructing \(\sqrt{75}\), the new hypotenuse \(\sqrt{76}\) is formed in a square root spiral, in which interval will it lie?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhile constructing a square root spiral, Riya draws a perpendicular segment of length 1 unit at the end of the previous hypotenuse of length \(\sqrt{8}\). She considers the new hypotenuse to be \(\sqrt{10}\). What should the correct new hypotenuse be?Class 9Number SystemsSquare root spiralLevel 20Medium MathematicsWhat type of number is √12 in a square-root spiral, and where is it located on the number line?Class 9Number SystemsSquare root spiralLevel 20Medium