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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 correct short proof idea for the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{2}), both (p) and (q) are found even. Why is this called a contradiction?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf assuming (\sqrt{5}) rational proves both (p) and (q) divisible by (5), what does this contradict?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhich option correctly states a difference between the proofs of (\sqrt{2}) and (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhy are (p) and (q) taken as coprime in all three proofs?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhich statement is wrong in the proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{3}), why can we not directly say (q) is divisible by (3) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf a student stops at only (p^2=2q^2) while proving (\sqrt{2}) irrational, why is the proof incomplete?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{5}), if (p=5k) and (q=5r) are obtained, which conclusion is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhich option gives the correct order of the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{2}), after getting (q^2=2k^2), which reasoning is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhere is the fact that (5) is prime used in the proof of irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf assuming (\sqrt{3}) rational makes both (p) and (q) divisible by (3), which fact is proved false?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhich option is a wrong conclusion in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{5}), after putting (p=5k), (25k^2=5q^2) is obtained. Which conclusion is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{3}), after putting (p=3k), (9k^2=3q^2) is obtained. What is the correct form of (q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIn the proof of (\sqrt{2}), after putting (p=2k), which equation follows from (p^2=2q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsIf (\sqrt{5}=\frac{p}{q}) is assumed in lowest form and (p^2=5q^2) is obtained, in which form should (p) be written?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium MathematicsWhile proving the irrationality of (\sqrt{3}), (p^2=3q^2) is obtained. Which conclusion about (p) with reason is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium Mathematics(\sqrt{2}) is assumed rational and written as (\sqrt{2}=\frac{p}{q}). If (p) and (q) are coprime, what is the correct next conclusion from (p^2=2q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Medium