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Irrationality

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (\sqrt{5}=\frac{a}{b}) and (a,b) are coprime, what is the first correct conclusion from (a^2=5b^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich statement is most essential in proving the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (\sqrt{2}) is assumed rational and written as (\sqrt{2}=\frac{p}{q}), where (p) and (q) are coprime, where does the contradiction mainly come from?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option gives the correct common structure of the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option best describes the correct common structure of the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsWhich option shows the common deeper idea in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsWhile proving the irrationality of (\sqrt{2}), if (\sqrt{2}=\frac{p}{q}) is assumed in lowest form, which reasoning from (p^2=2q^2) is most accurate?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsWhich option is the most useful precaution while writing an irrationality proof in an exam?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn an exam, which precaution is most important while writing the irrationality proof of (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium Mathematics(\sqrt{2}) is assumed rational and written as (\sqrt{2}=\frac{p}{q}). If (p) and (q) are coprime, what is the correct next conclusion from (p^2=2q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsWhich option is the common final idea in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIf (\sqrt{2}=\frac{p}{q}) is assumed in lowest form, what should be concluded first from (p^2=2q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIn the proof of (\sqrt{2}), if (q^2=2k^2) is obtained, what conclusion follows about (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsIn an exam, what should be clearly written in the last line of an irrationality proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsWhich option is the correct short reason for the irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsWhat is proved at the end in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsWhich method is common in proving the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsIn an exam, what should be clear in the final line while proving (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Easy MathematicsWhich option is the correct short reason for the irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Easy MathematicsWhich option is the correct short reason for the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Easy