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Square Root 2

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

MathematicsIf an answer writes √2 = a/b but does not mention gcd(a,b) = 1, what is the best comment?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “Since \((\sqrt{2})^2 = 2\) and 2 is rational, \(\sqrt{2}\) must also be rational.” What is the correct error in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option gives the most correct full logical chain in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “If the area of a square is rational, then its side must also be rational.” Which of the following examples disproves the statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student assumes that \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. On proceeding with the proof, the student finds that both \(a\) and \(b\) are even. What decisive conclusion follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, the student gets \(p^2=2q^2\). Which conclusion proves that this assumption is invalid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that if \(\sqrt{2}=\frac{p}{q}\), then both \(p\) and \(q\) may be even. Why is this statement incorrect in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich initial assumption is made to prove the irrationality of \(\sqrt{2}\) by the method of contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhy is the proof of \(\sqrt{2}\) valid without decimal expansion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich of the following statements is correct in the contradiction proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich statement correctly describes the contradiction obtained while proving that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student assumes that \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. From \(a^2=2b^2\), the student stops after concluding that \(a\) is even. Which conclusion is necessary to complete the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student says, “The square of \(\sqrt{2}\) is \(2\), and \(2\) is rational; therefore, \(\sqrt{2}\) is also rational.” What is the main error in this reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (√2), if (m) is assumed odd, what problem arises from (m²=2n²)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of \(\sqrt{2}\), if both \(m\) and \(n\) are even, what can be said about their highest common factor?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsRavi says that \(\sqrt{2}\) is irrational because its decimal expansion is infinite. What is the flaw in his argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf \(\sqrt{2}\) is assumed to be rational and written as \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, why does a contradiction arise in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof by contradiction for the irrationality of \(\sqrt{2}\), what is the main purpose of assuming \(\sqrt{2}=\frac{p}{q}\) in lowest terms?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf assuming (√2) rational gives a contradiction, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Easy MathematicsWhich statement correctly describes the main idea used in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium