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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।

MathematicsFor a square with side length 1 cm, Reena claims that its diagonal must also be rational because the side is rational. Which statement correctly identifies the error in Reena’s conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student claims that the diagonal of a square of side 1 unit is a rational number. Which argument correctly disproves this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(p/q\) be taken in lowest terms in a proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich statement correctly identifies why \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, which condition is essential when assuming \(\sqrt{2}=\frac{p}{q}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, after assuming \(p/q\) is in lowest terms, which condition directly contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsReena says, “The decimal expansion of \(\sqrt{2}=1.414213\ldots\) is infinite, so it is irrational.” What is the most accurate evaluation of her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsRima says, “\(\sqrt{2}\) is irrational because its decimal expansion is infinite.” What is the main flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that the decimal expansion of \(\sqrt{2}\) never terminates, so it is irrational. Which of the following arguments rigorously proves this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf a proof writes \(\sqrt{2}=\frac{m}{n}\) but does not state lowest form, what is the biggest weakness?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf \(m=2k\) and \(n^2=2k^2\), what is the combined conclusion in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsRavi claims that \(7+\sqrt{2}\) is a rational number because 7 is rational. What is the error in Ravi’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. Which conclusion from \(m^2=2n^2\) proves that this assumption is contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich of the following statements is an essential part of the proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof by contradiction that \(\sqrt{2}\) is irrational, suppose \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which final condition contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich skipped step would make the proof of \(\sqrt{2}\) incomplete?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsA student claims that \(3\sqrt{2}\) is rational because 3 is a rational number. What is the correct evaluation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. After obtaining \(p^2=2q^2\), which conclusion correctly advances the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof by contradiction that \(\sqrt{2}\) is irrational, why must \(p\) and \(q\) be chosen coprime when assuming \(\sqrt{2}=\frac{p}{q}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn the proof of \(\sqrt{2}\), if a student ends the proof after only writing \(a\) is even, what is the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard