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Irrational Numbers

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

MathematicsIt is known that \(\sqrt{3}\) is irrational. Which argument correctly completes a proof that \(\sqrt{12}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that sqrt3 is irrational, if sqrt3 = p/q is assumed to be in lowest terms, why does a contradiction arise?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich initial assumption is made to prove the irrationality of \(\sqrt{3}\) by the method of contradiction?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 MathematicsWhich of the following decimal expansions indicates an irrational number?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\) in lowest terms. If \(p\) is shown to be divisible by 3, which conclusion about \(q\) is needed to obtain a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, which statement produces the contradiction in the proof of its irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion produces a contradiction in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhat is the final contradiction in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium 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 MathematicsA student says, “\(\sqrt{3}=1.732\), so \(\sqrt{3}\) is a rational number.” What is the main error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option gives the correct final sentence in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf a prime number has an odd exponent in the prime factorisation of a number, what can be concluded about the square root of that number?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 MathematicsWhich of the following numbers cannot be written as a ratio \(p/q\) of two integers, where \(q\ne0\)?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 MathematicsWhich option is a wrong start in the proof of \(\sqrt{2}\)?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