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Prime Factorization

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

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 MathematicsWhat is the idea of prime factors of a perfect square in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof by contradiction for the irrationality of \(\sqrt{3}\), assume \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. Which conclusion from \(p^2=3q^2\) is essential for the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhich statement gives the deeper reason using prime exponents in perfect squares for the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich idea about exponents of prime factors deeply explains the irrationality of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich idea about exponents of prime factors deeply explains the irrationality of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhat is the deeper prime-factor reason in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich option gives the deeper prime-factor reason for irrationality of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option states the correct hidden principle used in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf a rational number \(\frac{p}{q}\) is in lowest terms, which condition is necessary and sufficient for its decimal expansion to terminate?Class 9Number SystemsDecimal representationLevel 11Expert MathematicsIf the rational number \(\frac{p}{q}\) is in lowest form and \(q>0\), when does its decimal expansion terminate?Class 9Number SystemsDecimal representationLevel 11Expert MathematicsWhen does a fraction \(\frac{p}{q}\) in lowest terms have a terminating decimal expansion?Class 9Number SystemsDecimal representationLevel 12Medium MathematicsWhich of the following fractions, in its lowest form, has a terminating decimal expansion?Class 9Number SystemsDecimal representationLevel 15Easy MathematicsA student says that the decimal expansion of \(\frac{7}{30}\) will terminate because 30 is an even number. Which is the correct analysis of the error?Class 9Number SystemsDecimal representationLevel 15Easy