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Number Systems

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

MathematicsHow can the proof of (\sqrt{3}) be expressed in the language of infinite descent?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsHow can the proof of (\sqrt{2}) be understood from the viewpoint of infinite descent?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 MathematicsIf (\sqrt{2}) is rational and (\frac{a}{b}) is in lowest form, by which principle is both (a,b) even impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student says, “Since 1.732 is a terminating decimal, \(\sqrt{3}\) is rational.” Which option correctly identifies the error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student claims that \(5+\sqrt{3}\) is a rational number. Which argument correctly disproves the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy is it necessary to prove (q) divisible by (3) after taking (p=3r) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich assumption is made at the beginning to prove the irrationality of \(\sqrt{3}\) by contradiction?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 MathematicsIn a proof by contradiction, assume that \(\sqrt{3}=\frac{m}{n}\), where \(m\) and \(n\) are coprime integers. If \(3n^2=m^2\) is obtained, which conclusion decisively shows that this assumption is impossible?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 MathematicsReema says, “\(\sqrt{3}\approx1.732\); therefore, \(\sqrt{3}\) is rational because 1.732 is rational.” What is the correct evaluation of Reema’s argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose it is claimed that \(s=\sqrt{2}+\sqrt{3}\) is rational. Since \((\sqrt{2}+\sqrt{3})(\sqrt{3}-\sqrt{2})=1\), \(\sqrt{3}-\sqrt{2}=1/s\) would also be rational. Which equation below immediately produces a contradiction from this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\), a student assumes \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime. After obtaining \(a^2=3b^2\), the student states that both \(a\) and \(b\) are divisible by 3. Which reasoning is necessary to justify this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn irrationality of (\sqrt{3}), which statement alone does not complete the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn irrationality of (\sqrt{2}), which statement does not complete the proof because it is only half of the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard 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 MathematicsIt is known that \(\sqrt{3}\) is irrational. Which of the following conclusions must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn the proof of (\sqrt{3}), both (a) and (b) being divisible by (3) breaks which initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich initial assumption is required when proving the irrationality of \(\sqrt{3}\) by the contradiction method?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard