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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।

MathematicsHow can (p^2=3q^2) in the proof of (\sqrt{3}) be understood using exponents of prime factors?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIn the proof of (\sqrt{3}), which statement is correct but not the final conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhat is the purpose of substituting (p=3k) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option correctly identifies the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option correctly completes the proof of irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIf in the proof of (\sqrt{3}), both (p) and (q) are divisible by (3), what is the effect on the lowest form of (\frac{p}{q})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option is a wrong algebraic simplification in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option disturbs the logical order in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIf a student writes (3=\frac{p}{q}) directly from (\sqrt{3}=\frac{p}{q}), what is the correct correction?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIn the proof of (\sqrt{3}), what is the basis for writing (q=3r) after getting (q^2=3k^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIn the proof of (\sqrt{3}), if (p=3r) and (q=3s), what is definite about (\gcd(p,q))?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIn the proof of (\sqrt{3}), after putting (p=3k), which middle equation is correct from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsAssume (\sqrt{3}) is rational and write (\sqrt{3}=\frac{p}{q}). What is the correct reasoning about (p) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsWhich option gives the correct further reasoning after substituting (p=3k) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIn the proof of irrationality of (\sqrt{3}), which statement should come just before the final conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIn the proof of (\sqrt{3}), if (p) is divisible by (3) from (p^2=3q^2), what type of number is (k) in (p=3k)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIf (\sqrt{3}) is assumed rational and (\frac{p}{q}) is in lowest form, what conclusion follows when both (p) and (q) are found divisible by (3)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIf in the proof of (\sqrt{3}), both (p) and (q) turn out divisible by (3), which greatest common divisor condition definitely breaks?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIf in the proof of (\sqrt{3}), both (p) and (q) are found divisible by (3), which statement about (\frac{p}{q}) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsWhich option is a wrong proof method in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard