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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।

MathematicsIf the hypotenuse formed after \(\sqrt{n}\) in a square root spiral is (25), what is the value of (n)?Class 9Number SystemsSquare root spiralLevel 20Hard MathematicsA student says that in a square root spiral, each new hypotenuse is exactly 1 unit longer than the previous hypotenuse. Which correction is correct?Class 9Number SystemsSquare root spiralLevel 20Hard 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 spiralLevel 20Hard 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 spiralLevel 20Hard MathematicsIf a \(3\) unit perpendicular is used instead of \(1\) unit in the usual square root spiral, what will be the hypotenuse formed from \(\sqrt{n}\)?Class 9Number SystemsSquare root spiralLevel 20Hard 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 spiralLevel 20Hard MathematicsWhich conclusion is correct for locating the point at a distance \(\sqrt{50}\) on the number line using a square root spiral?Class 9Number SystemsSquare root spiralLevel 20Hard MathematicsIn a standard square root spiral, which of the following lengths is not obtained as a radial segment?Class 9Number SystemsSquare root spiralLevel 19Hard MathematicsIn a square root spiral, point P corresponding to \(\sqrt{18}\) is marked. Riya says that P will lie between 4 and 5 units from the centre O. What is the correct evaluation of Riya's statement?Class 9Number SystemsSquare root spiralLevel 19Hard 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 spiralLevel 19Hard MathematicsWhich feature of the construction of a square root spiral is correct?Class 9Number SystemsSquare root spiralLevel 19Hard 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 spiralLevel 19Hard MathematicsBefore placing \(\sqrt{440}\) on the number line using a square root spiral, which interval is correct?Class 9Number SystemsSquare root spiralLevel 19Hard 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 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 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 MathematicsWhich statement is correct about the point representing \(\sqrt{49}\) in a square root spiral?Class 9Number SystemsSquare root spiralLevel 19Hard