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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।

MathematicsIf ext{\(\sqrt{3}\)} is assumed to be ext{\(\frac{p}{q}\)}, where ext{\(p\)} and ext{\(q\)} are coprime, which conclusion produces the contradiction in a proof by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student assumes that \(3\sqrt{2}\) is a rational number. Which argument correctly shows a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich of the following statements is correctly used in the proof that sqrt(3) is irrational in number systems?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf \(p/q\) is in lowest terms and \(p^2=3q^2\), which conclusion establishes the contradiction in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert 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 of the following is the valid next inference?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. From \(p^2=3q^2\), which conclusion about \(p\) is necessary?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhat is the highest-level description of the similarity between the proofs of √2 and √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhy is divisibility reasoning necessary instead of approximate decimal in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhy is the coprime fraction argument better than decimal approximation in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student assumes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, to prove that \(\sqrt{3}\) is irrational. After obtaining \(3q^2=p^2\), the student says, “\(p\) is divisible by 3, so a contradiction has been reached.” Which statement correctly identifies the gap in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf a contradiction is obtained after assuming that √2 is rational, according to logic which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of (\sqrt{3}), what is the role of (n\neq0), and where does the final contradiction come from?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of √2, writing y ≠ 0 is necessary, but why does it not give the final contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhat is the idea of prime factors of a perfect square in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhat is the idea of prime factors of a perfect square in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion creates the contradiction in the proof by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student assumes that \(\sqrt{3}\) is rational and writes it as \(\frac{p}{q}\) in lowest terms, where \(p\) and \(q\) are coprime. Which conclusion correctly follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhy is writing (p=3q) from (p^2=3q^2) unacceptable in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. During the proof, the student obtains \(p^2=3q^2\). What is the correct conclusion needed to establish a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that if \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=2q^2\) implies only that \(p\) is even; nothing can be concluded about \(q\). What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert