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Number Systems

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

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 spiralLevel 19Hard MathematicsAfter obtaining \(\sqrt{18}\) using the square root spiral, Riya marks it at 4.5 on the number line. Which comment about her marking is correct?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsTo construct √224 in a square root spiral, what is the correct previous hypotenuse and in which interval will the formed hypotenuse lie?Class 9Number SystemsSquare root spiralLevel 19Hard 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 spiralLevel 19Hard MathematicsIn a square root spiral, the length of the segment drawn from the origin to an outer vertex is \(\sqrt{n}\). For which type of \(n\) will this length be a rational number?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsIn a square root spiral, which of the following labelled hypotenuses represents a rational length?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsIn a square root spiral, if the new hypotenuse is √(n+1) and it is the whole number 12, what was the previous hypotenuse?Class 9Number SystemsSquare root spiralLevel 19Medium MathematicsWhile constructing a square root spiral, a student says that \(\sqrt{26}\) should be shown at the point 5 because 26 is very close to 25. What is the correct correction of this error?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsAt a step in a square root spiral, the hypotenuse is √m. If m is exactly 1 less than a perfect square, what will the next hypotenuse be like?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhich statement is correct about the point representing \(\sqrt{49}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard 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 MathematicsWhich statement is correct when comparing \(\sqrt{242}\) and \(\sqrt{256}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsIn a square root spiral, why does the next hypotenuse after √168 simplify specially?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhile forming √4 from √3 in a square root spiral, which statement contains a logical error?Class 9Number SystemsSquare root spiralLevel 19Medium 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 MathematicsIn a square root spiral, if the previous hypotenuse is √80 and the new perpendicular is 1 unit, at what exact value will the new hypotenuse lie?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