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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।

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, √5Hard MathematicsWhich option correctly identifies the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich statement is true but given with a wrong reason in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard 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, √5Hard MathematicsWhich option gives a result against (\gcd(p,q)=1) in the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{2}), if (p=2k) and (q=2r), how can (\frac{p}{q}) be reduced?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard 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, √5Hard MathematicsIn the proof of (\sqrt{5}), after getting (p^2=5q^2), which conclusion cannot be drawn immediately?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich statement shows a logical weakness in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich option shows the common deeper idea in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf assuming (\sqrt{2}) rational finally makes (\frac{p}{q}) not remain in lowest form, what is the correct conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIn the proof of (\sqrt{5}), (q) is divisible by (5) from (q^2=5k^2). Which condition is necessary for this conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich statement correctly describes the difference between the proofs of (\sqrt{2}) and (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich option gives a correct and complete reasoning in the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard 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, √5Hard MathematicsIn the proof of (\sqrt{2}), after getting (p^2=2q^2), which statement is correct but does not yet complete the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhy is it necessary to assume (p) and (q) coprime while proving (\sqrt{5}) irrational?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsWhich option is a wrong proof method in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsAfter proving both (p) and (q) even in the proof of (\sqrt{2}), how should the final conclusion be written?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard MathematicsIf the sequence (p^2=5q^2), (p=5k), (q^2=5k^2) appears in the proof of (\sqrt{5}), what is the next correct statement?Class 10Real NumbersProof of irrationality of √2, √3, √5Hard