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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।

MathematicsWhat is the best exam formula for proving irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), after getting (3\mid p) and then (3\mid q), which statement would be false?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (\sqrt{2}) is assumed rational and finally both (p,q) turn out even, which conclusion is logical?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), both (a) and (b) are found divisible by (5). What type of result is this?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich statement is unnecessary in the proof of irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (p) and (q) are coprime, why is it impossible to get both (p=2m) and (q=2n)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich property of rational numbers is used in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), if someone writes (a=25k) from (5\mid a^2), what is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (\sqrt{3}) were rational, what impossible situation would appear at the end of the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{2}), (p^2=2q^2) shows (p^2) is even. If (p) is assumed odd, what problem occurs?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich statement starts the proof of irrationality of (\sqrt{5}) most clearly?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{3}), after putting (p=3k), (9k^2=3q^2) is obtained. What is the correct simplification?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (n) is an odd integer, then (n^2) is odd. This fact is especially useful in which proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), what is the correct intermediate conclusion needed to write (a=5k) from (a^2=5b^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option gives the correct basis for proving (q) even in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf both (p) and (q) are found divisible by (3) in proving (\sqrt{3}) irrational, which statement about (\frac{p}{q}) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIn the proof for (\sqrt{5}), while writing (5\mid b) from (5\mid b^2), what must be added?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich conclusion should be written at the very end of the proof of irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsIf (p^2=3q^2) in the proof for (\sqrt{3}), what is the simple reason that (p^2) is divisible by (3)?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert MathematicsWhich option correctly explains proof by contradiction?Class 10Real NumbersProof of irrationality of √2, √3, √5Expert