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Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIn the proof that \(\sqrt{3}\) is irrational, \(a^2=3b^2\) gives \(3\mid a^2\). Which rule justifies the next step?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. After concluding from \(p^2=3q^2\) that \(p\) is divisible by 3, which conclusion completes the contradiction proving \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn a proof by contradiction that \(\sqrt{3}\) is irrational, what fact produces the contradiction after assuming \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime integers?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf sqrt{2} is an irrational number, which of the following numbers must also be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says, “3 is a rational number, so \(\sqrt{3}\) must also be rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of (\sqrt{3}), why does (p^2) divisible by (3) imply (p) divisible by (3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsBefore assuming \(\sqrt{3}=\frac{p}{q}\) in a proof by contradiction that \(\sqrt{3}\) is irrational, which condition on \(p\) and \(q\) is essential?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf √3 were rational, which statement about p/q should be correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (\sqrt{2}) were rational, what condition should hold for (\frac{a}{b})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option shows the correct algebraic chain in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRima says that \(5+\sqrt{2}\) is a rational number because 5 is rational. Which is the correct evaluation of her statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of √3, after both p and q become divisible by 3, what is the final conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRiya assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, she gets \(p^2=3q^2\). Which argument correctly proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn which of the following options are both numbers irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf a student assumes both (p) and (q) divisible by (3) immediately after writing (\sqrt{3}=\frac{p}{q}), what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf a student writes (\sqrt{2}=\frac{a}{b}) and assumes (a) and (b) even from the start, what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option correctly states the main difference between the proofs of (\sqrt{2}) and (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (p^2=3q^2) and (p=3k), why will (q) be divisible by (3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (a^2=2b^2) and (a=2r), why will (b) be even?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(4+\sqrt{3}\) is a rational number because 4 is rational. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium