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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 the square of an integer (n) is even, then (n) is even. How many times is this fact used in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich statement correctly uses the primality of (5) in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), if someone writes (a=3b) directly from (3\mid a^2), what is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich statement shows that the proof of irrationality of (\sqrt{2}) is not based on decimals?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf assuming (\sqrt{5}) rational gives (x^2=5y^2), after writing (x=5n), toward which conclusion does the proof move?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option states the correct final contradiction 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) are proved even, which statement about (\frac{p}{q}) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), after putting (x=5n), (25n^2=5y^2) is obtained. What is the next correct simplification?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), after getting (b^2=3m^2), what conclusion about (b) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (r) is prime and (\sqrt{r}=\frac{p}{q}) is assumed in lowest form, which equation is obtained after squaring?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich structure remains common in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf a student writes only (\sqrt{5}\approx2.236) to prove rationality or irrationality, why is this argument incomplete?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), after putting (a=3m), into what form does (a^2=3b^2) change?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option is the most serious error in the proof of irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (p) and (q) are coprime, what does obtaining (5\mid p) and (5\mid q) in the proof for (\sqrt{5}) indicate?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), the conclusion (3\mid a) from (3\mid a^2) is based on which principle?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{2}), after getting (q^2=2k^2), which conclusion helps complete the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (\sqrt{5}) is assumed rational and written as (\sqrt{5}=\frac{x}{y}), which algebraic step correctly leads to (x^2=5y^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhile proving the irrationality of (\sqrt{3}), what weakness occurs if (a) and (b) in (\sqrt{3}=\frac{a}{b}) are not taken coprime?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsAfter assuming (\sqrt{2}=\frac{p}{q}) in lowest form and getting (p^2=2q^2), why is it correct to write (p=2k)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert