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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।

MathematicsIf (a^2=3b^2) is obtained in proving (\sqrt{3}) irrational, why is it correct to say (a^2) is a multiple of (3)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), which condition is necessary while taking (5\mid y) from (5\mid y^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option correctly explains the parity idea in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (3\mid a) and (3\mid b), what contradiction arises with assuming (\frac{a}{b}) in lowest form?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhile taking (x) and (y) coprime in the proof for (\sqrt{5}), what must be kept in mind?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf someone says (\sqrt{2}) is irrational because (2) is even, what is the correct correction?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option gives the correct reasoning to reach (q) in the proof for (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{2}), when both (p) and (q) turn out even, which initial statement is proved false?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsHow does (5) not being a perfect square help in understanding the irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (a) and (b) are coprime but the proof gives (a=3m) and (b=3n), what conclusion follows?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option shows the correct order for proving the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{2}), if both (p) and (q) are even, by which number can the fraction be further reduced?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf someone writes (q^2=4k^2) after putting (p=2k) in (p^2=2q^2), where is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich statement correctly generalizes the proof of irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the irrationality proof of (\sqrt{5}), what idea is hidden in moving from (5\mid x^2) to (x=5m)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option directly conflicts with (p) and (q) being coprime in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf no contradiction appears while proving (\sqrt{3}) irrational by assuming it rational, which condition is probably missing?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), if both (x) and (y) turn out divisible by (5), what can be said about (\gcd(x,y))?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich opening sentence is most complete for proving the irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proofs of (\sqrt{3}) and (\sqrt{5}), which prime factors appear respectively instead of (2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert