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Proof Of Irrationality Of 2 3 5

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

MathematicsIf assuming (\sqrt{3}) rational gives (a^2=3b^2), what must be shown about (a) and (b) at the end?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhat is the role of assuming coprime numbers in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{5}), after putting (m=5k), which equation follows from (m^2=5n^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf (r) is prime and (r\mid x^2), which rule is used in irrationality proofs?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhich statement is a wrong step in the proof of irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{3}), after putting (a=3t), which form of (b^2) follows from (a^2=3b^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{2}), if (p=2r), how does (p^2=2q^2) change?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf assuming (\sqrt{5}=\frac{m}{n}) and squaring gives (m^2=5n^2), what is the correct next form for (m)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsAssume (\sqrt{3}) is rational and (\sqrt{3}=\frac{a}{b}). If (a) and (b) are coprime, when will a contradiction occur in the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium 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, √5Medium MathematicsWhich option best describes the common idea in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsWhich option correctly shows the breaking of the coprime condition in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsIn the proof of (\sqrt{5}), if (q^2=5k^2) is obtained, what is the next correct conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsIn the proof of (\sqrt{3}), if (q^2=3k^2), what is the correct conclusion about (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy 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, √5Easy MathematicsIn an exam, what should be clearly written in the last line of an irrationality proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsWhich statement is correct for the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsIn the proof of (\sqrt{5}), both (p) and (q) are found divisible by (5). This is against what?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsWhich option shows that (p) and (q) are not coprime?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy MathematicsWhich option is the correct final sentence to complete the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Easy