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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।

MathematicsWhich option correctly states the effect of both (p) and (q) being divisible by (3) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsIn the proof of (\sqrt{3}), if (p=3k), what is the correct value of (p^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsA student writes (\sqrt{3}=\frac{p}{q}), so (3=\frac{p}{q}). What is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsWhich option is the correct short proof idea for the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium 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, √5Level 17Medium MathematicsWhich option gives the correct order of the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium 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, √5Level 17Medium 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, √5Level 17Medium 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, √5Level 17Medium MathematicsIn the proof of (\sqrt{3}), from (p^2=3q^2), (p) is divisible by (3). This is based on which rule?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIf (\sqrt{3}) is assumed rational and written as (\frac{p}{q}), what is the benefit of taking (\frac{p}{q}) in lowest form?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsWhich statement correctly tells the final conclusion about (b) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIn the proof of (\sqrt{3}), which step is done to remove the square root?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIn the proof of (\sqrt{3}), what does getting (p=3r) and (q=3s) show?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsWhich option gives the correct reason for writing (a=3k) in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsAfter assuming (\sqrt{3}) rational, (\sqrt{3}=\frac{p}{q}) is written. If common factor (3) is found in (p) and (q), which assumption is proved false?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsWhich statement is correct in the proof of (\sqrt{3}) but is not the main step in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIf assuming (\sqrt{3}) rational gives (a^2=3b^2), what must be shown about (a) and (b) at the end?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIn the proof of (\sqrt{3}), after putting (a=3t), which form of (b^2) follows from (a^2=3b^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsAssume (\sqrt{3}) is rational and (\sqrt{3}=\frac{a}{b}). If (a) and (b) are coprime, when will a contradiction occur in the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium