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Square Root 3

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 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 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 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 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 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 MathematicsIn a proof by contradiction, a student assumes \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. After obtaining \(p^2=3q^2\), which statement correctly justifies the conclusion \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhich assumption is required at the beginning of a proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsA student believes that for some non-zero rational number \(q\), \(q\sqrt{3}\) can be rational. Which argument correctly refutes this belief?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIn a proof of irrationality, if 3 is prime and 3 divides the square p² of an integer p, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), then \(p^2=3q^2\) only implies that \(p\) is divisible by 3; nothing can be concluded about \(q\). What is the student's error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms and \(p^2=3q^2\) is obtained, which conclusion establishes the contradiction in the proof of irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\frac{p}{q}\) is in lowest terms, which immediate conclusion follows from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, assume that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. Which conclusion from \(p^2=3q^2\) is necessary to reach a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsUsing exponents of prime factors in perfect squares, which idea is correct in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf \(p\) and \(q\) are coprime integers and \(p^2=3q^2\), which conclusion is essential in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of √3, after which sequence is n proved divisible by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsRima assumes that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which conclusion in her proof establishes a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that \(2+\sqrt{3}\) is a rational number. Which argument correctly disproves the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert