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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।

MathematicsIn the proof of (\sqrt{3}), if someone writes directly from (p^2=3q^2) that (q) is divisible by (3), which analysis is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, assume that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. Which conclusion creates a contradiction to the initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option correctly uses the prime factor idea in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option shows the correct contrapositive-style use needed in proving √2 irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf (p^2=3q^2) and (p=3k), what combined conclusion about (p) and (q) follows from (q^2=3k^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf (a^2=2b^2) and (a=2r), what combined conclusion about (a) and (b) follows from (b^2=2r^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “Since \((\sqrt{2})^2 = 2\) and 2 is rational, \(\sqrt{2}\) must also be rational.” What is the correct error in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of √2, why is assuming a and b coprime more than a formality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, which situation contradicts the assumption that \(p/q\) is in lowest terms?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option gives the most correct full logical chain in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of (\sqrt{3}), if (p) is not divisible by (3), why does (p^2=3q^2) create conflict?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich statement is correct in the proof of the irrationality of \(\sqrt{3}\), based on \(a^2=3b^2\), where \(a\) and \(b\) are coprime integers?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof by contradiction, assume that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Why does this assumption lead to a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsSuppose \\(\sqrt{3}=\frac{p}{q}\\), where \\(p\\) and \\(q\\) are coprime positive integers. Which conclusion from \\(p^2=3q^2\\) gives the contradiction needed to prove that \\(\sqrt{3}\\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “If the area of a square is rational, then its side must also be rational.” Which of the following examples disproves the statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf √2 = a/b is in lowest form, what does proving that both a and b are even show?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of (\sqrt{3}), which conclusion alone is not sufficient but is the first step toward final contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich statement creates the actual contradiction with the coprime condition in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf n² is divisible by 3 for an integer n, which statement about n must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if it is shown that 3 divides both \(a\) and \(b\), which conclusion creates the contradiction in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard