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

MathematicsIf \(p\) and \(q\) are coprime integers and \(p^2=3q^2\), which conclusion is essential in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of √3, after which sequence is n proved divisible by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsRima assumes that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which conclusion in her proof establishes a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhat is the main mistake in writing (m=3n) directly from (m^2=3n^2) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 55Expert MathematicsA student claims that \(2+\sqrt{3}\) is a rational number. Which argument correctly disproves the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. Which of the following properties is crucial for proving that this assumption is contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf √2 = r/s is in lowest form and finally 2 divides r and 2 divides s, which statement is the most precise contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhy is only (m) being divisible by (3) incomplete in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhy is only (r^2) being even not the final contradiction in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of √3, after taking m = 3k, which step from m² = 3n² proves n divisible by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsAarav assumes that \(\sqrt{3}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. After obtaining \(m^2=3n^2\), he says that divisibility of \(m^2\) by 3 does not prove that \(m\) is divisible by 3. Which fact corrects Aarav’s error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that \(\sqrt{2}+\sqrt{3}\) is rational. Which argument correctly proves that the claim is wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student calls \(\sqrt{2}\) irrational after seeing its decimal form 1.414213... . Which property must be proved to justify the conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhile starting a proof by contradiction for the irrationality of \(\sqrt{2}\), Riya assumes that \(\sqrt{2}=p/q\), where \(p\) and \(q\) are integers. Which additional condition on \(p\) and \(q\) is necessary to make the proof valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIf the contradiction proof of \(\sqrt{2}\) succeeds, what is the final logical conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf \(n\) is an integer and \(3\mid n^2\), which conclusion used in the proof of the irrationality of \(\sqrt{3}\) is certainly true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhat is the most essential exam caution in proving irrationality of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIn the proof of √3, which statement is a middle step rather than the final conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIn the proof of (\sqrt{2}), which statement is a middle step rather than the final conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhich statement can be a wrong but tempting answer in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert