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Irrationality Proof

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

MathematicsA student claims that if \(3p^2=q^2\), then \(p\) must be divisible by 3. What is the correct evaluation of the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf (h) is not divisible by (3) and (h^2=3k^2), what inconsistency appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn the contradiction proof of the irrationality of \(\sqrt{3}\), what does writing \(\frac{p}{q}\) in lowest terms mean?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student claims that if the square of an integer is divisible by 2, then the integer itself is divisible by 2. Which argument correctly supports this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf a contradiction is obtained after assuming that √2 is rational, according to logic which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\frac{p}{q}\) is in lowest terms, which immediate conclusion follows from \(3\mid p^2\)?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 MathematicsIf someone writes (p=3q) from (p^2=3q^2), what is the correct correction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIf someone writes (a=2b) from (a^2=2b^2), what is the correct correction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhat is the most important exam caution in the proofs of √2 and √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf a student tries to prove irrationality of √2 by writing its decimal value, what is the correct evaluation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf p is not divisible by 3 in p² = 3q², what contradiction appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf (a) is assumed odd in (a^2=2b^2), what contradiction appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIn the proof of (\sqrt{3}), both (a) and (b) being divisible by (3) breaks which initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf a proof writes \(\sqrt{2}=\frac{m}{n}\) but does not state lowest form, what is the biggest weakness?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student claims that if the square of an integer is divisible by 3, then the integer itself is divisible by 3. What is the correct evaluation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf the square of an integer is divisible by 3, which conclusion about the integer must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf both \(x,y\) are even, why is \(\frac{x}{y}\) considered reducible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich skipped step would make the proof of \(\sqrt{2}\) incomplete?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf (x,y) are coprime and both are proved even, what is the correct contradiction about (\gcd(x,y))?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard