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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।

MathematicsA student says that \(\sqrt{13}\) cannot be represented on a square root spiral because 13 is not a perfect square. Which option correctly corrects the statement?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 MathematicsIn a square root spiral, the line segment representing \(\sqrt{7}\) lies between which two consecutive whole numbers?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 MathematicsIn a square root spiral, how long is the new perpendicular side usually kept in each new triangle?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 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 MathematicsIf \(x=\sqrt{2}+\sqrt{3}\), which argument correctly disproves the assumption that \(x\) is rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. On squaring, the student gets \(p^2=3q^2\) and concludes that \(p\) is divisible by 3. What is the next essential step to complete the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhy is it necessary to take the fraction \(\frac{p}{q}\) in lowest terms in the contradiction proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, which property is used to conclude \(3\mid p\) from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student says that \(\sqrt{3}\) is irrational because its decimal expansion \(1.732\ldots\) continues endlessly. What is the main error in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf a student assumes that \(\sqrt{2}+\sqrt{3}\) is a rational number \(r\), which conclusion correctly proves a contradiction in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student claims that \(\sqrt{2}+\sqrt{3}\) is a rational number. Which argument correctly identifies the error in the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert