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Square Root Spiral

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, 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 MathematicsWhy does adding a (1) unit perpendicular to hypotenuse (\sqrt{n}) in a square root spiral give new hypotenuse (\sqrt{n+1})?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhile identifying the interval of (\sqrt{195}) in a square root spiral, which mistake is most likely?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhich of the following sequences is most correct for constructing \(\sqrt{10}\) in a square root spiral?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 MathematicsWhy is using (\sqrt{46}) and a (2) unit perpendicular wrong for constructing (\sqrt{48}) by the usual rule of square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhat is the correct position of (\sqrt{288}) in a square root spiral?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 when comparing the hypotenuse formed after (\sqrt{63}) and (\sqrt{65}) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsWhat is the correct reason for constructing (\sqrt{8}) from (\sqrt{7}) and (1) in a square root spiral?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 MathematicsIf the new hypotenuse in a square root spiral is (\sqrt{226}), what was the immediately previous hypotenuse and in which interval does the new value lie?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