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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।

MathematicsWhich option is the biggest common misconception in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{3}), after getting (q^2=3k^2), why can (q=3r) be written?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf (r) is prime and (r\mid x^2), what is its correct use in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich statement gives the correct basis for proving (q) even in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{5}), if both (p) and (q) are proved divisible by (5), which conclusion is the most logical?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf a student writes (3=\frac{p}{q}) from (\sqrt{3}=\frac{p}{q}), what is the correct correction?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich option states the final contradiction in the proof of (\sqrt{2}) in correct language?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{5}), (p) is proved divisible by (5) from (p^2=5q^2). What does this depend on?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf assuming (\sqrt{3}) rational gives (p^2=3q^2), which is the correct chain until (q) is proved divisible by (3)?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhat completes the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich option shows an algebraic mistake in the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{3}), (p^2=3q^2) gives (p=3k) and then (q=3r). Why does this make the original assumption false?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{2}), if someone says that (p^2=2q^2) immediately makes both (p) and (q) even, what is the correct comment?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf (p) and (q) are coprime, which result would most directly contradict this?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich step is wrong in order in the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf (p=3r) and (q=3s) are obtained in the proof of (\sqrt{3}), what is the most appropriate contradiction?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{2}), after putting (p=2r), which correct simplification is obtained from (p^2=2q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf (\sqrt{5}=\frac{p}{q}) is assumed in lowest form and (p=5k) is obtained in the proof, what is the next important aim?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{3}), what is the proper basis for writing (p=3k) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard 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, √5Hard