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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।

MathematicsIn a square root spiral, after (\sqrt{8}), which hypotenuse is obtained by adding a (1) unit perpendicular?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, which side is generally kept of length 1 unit to construct each new right triangle?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsA square root spiral helps to represent what kind of numbers on the number line?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, the line segment representing \(\sqrt{7}\) lies between which two consecutive whole numbers?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsStarting from (\sqrt{1}) in a square root spiral, which is the third hypotenuse?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsWhy is each new 1-unit line segment drawn perpendicular to the previous hypotenuse in a square root spiral?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsWhich theorem is mainly used to find the hypotenuse in a square root spiral?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, how long is the new perpendicular side usually kept in each new triangle?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsEach new triangle in a square root spiral is of which type?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, after the hypotenuse (\sqrt{3}), which length is obtained by adding a (1) unit perpendicular?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIf a perpendicular of length 1 unit is drawn at the end of a hypotenuse of length √2, what will be the length of the next hypotenuse?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, what is the hypotenuse of the first right triangle made with base (1) unit and perpendicular (1) unit?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn a square root spiral, which segment is drawn at the end of the previous hypotenuse to form a new right triangle?Class 9Number SystemsSquare root spiralLevel 22Easy MathematicsIn the proofs of √2 and √3, what should not be treated as the basis of proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsReema says that if \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=2q^2\) only shows that \(p\) is even; therefore \(\sqrt{2}\) is not proved irrational. Which essential point is missing from Reema's argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn the standard proof by contradiction, suppose that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. From \(p^2=3q^2\), which deduction is essential for obtaining the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich condition guarantees that the square root of a natural number \(n\) is rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student claims that \(\sqrt{3}\) is rational because its decimal form is 1.732 and \(1.732=\frac{1732}{1000}\). What is the error in the student’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, if \(\sqrt{2}=\frac{p}{q}\) where \(p\) and \(q\) are coprime, which conclusion necessarily follows from \(p^2=2q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsRima says, “\(\sqrt{3}=1.732\); therefore, \(\sqrt{3}\) is rational.” What is the main error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert