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Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

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, √5Level 17Expert MathematicsHow does (5) not being a perfect square help in understanding the irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert MathematicsWhich statement correctly uses the primality of (5) in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert 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, √5Level 17Expert MathematicsWhich statement is not correct in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich option is unnecessary in the proof of irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIf (p) and (q) are coprime, why can (p=5m) and (q=5n) not hold together?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsAssuming (\sqrt{5}) rational gives (p^2=5q^2). If (p=5r), which simplification is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhy is it impossible for both (p) and (q) to be divisible by (5) in the irrationality proof of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIn the proof of (\sqrt{5}), after proving from (p^2=5q^2) that (p) is divisible by (5), what is the next correct step?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich difference is correct when comparing the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich option is only an incomplete hint for the irrationality of (\sqrt{5}), not a full proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich statement gives the correct contradiction at the end of the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert