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Sqrt3 Proof

Class 10 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}), after getting (q^2=3k^2), why can (q=3r) be written?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard 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, √5Level 16Hard 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, √5Level 16Hard 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, √5Level 16Hard 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, √5Level 16Hard 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, √5Level 16Hard MathematicsWhich idea works similarly in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIf in the proof of (\sqrt{3}), both (p) and (q) are divisible by (3), what can be said about (\frac{p}{q})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhich option is a wrong simplification in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhich option completes the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhich statement gives the correct basis for writing (p=3k) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), after getting (q^2=3k^2), which form can be written for (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), if (p=3k) and (q=3r) are obtained, what is the correct conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), why is (q) not directly said to be divisible by (3) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIf (\sqrt{3}) were rational, how would it be written in lowest form?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), if both (p) and (q) are found divisible by (3), what does this contradict?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), after putting (p=3k), how does (p^2=3q^2) change?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), after assuming (\sqrt{3}=\frac{p}{q}), which correct equation is obtained by squaring?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhich option is the correct chain to reach (q) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsIf (q^2=3k^2) is obtained in the proof of (\sqrt{3}), what is the correct conclusion for (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium