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Real Numbers

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

MathematicsIf (\sqrt{5}=\frac{x}{y}) and (x,y) are coprime, which conclusion follows immediately from (x^2=5y^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhen (\sqrt{3}) is assumed rational and written as (\sqrt{3}=\frac{a}{b}), why are (a) and (b) taken coprime?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIf (\sqrt{2}=\frac{p}{q}) is assumed in lowest form and (p^2=2q^2) is obtained, what is the most precise reason that (p) is even?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich conclusion is correct for all three numbers (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option is a wrong conclusion in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (x^2) is even, what is the correct conclusion about (x)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich statement is true in both proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (\sqrt{2}) were rational, why would its form (\frac{p}{q}) finally be rejected?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhy is (5\mid b) concluded from (5\mid b^2) in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option best expresses the main idea behind the irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf both (p) and (q) are divisible by (3), what can be said about (\frac{p}{q})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich type of proof is most commonly used to prove the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich statement gives the final conclusion about (q) in the proof for (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf a student does not write (q\neq0) while proving (\sqrt{2}) irrational, what is missing?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option is a correct example of an irrational square root because it is not a perfect square?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option clearly shows that assuming (\sqrt{5}) rational is wrong?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIn the proof for (\sqrt{3}), if (p=3k), what is (p^2) equal to?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (p,q) are coprime in (\sqrt{2}=\frac{p}{q}), what does it indicate when both (p) and (q) turn out even?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option correctly explains proof by contradiction in irrationality proofs?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich property in the proof of (\sqrt{2}) is directly connected with (2) being prime?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard