Skip to content

Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

RELATED QUESTIONS

Irrational Numbers

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

MathematicsA student claims that \(\sqrt{3}\) is rational and writes it as \(\frac{p}{q}\) in lowest terms, where \(p,q\) are coprime. If \(p^2=3q^2\), what is the error in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, \(p^2=2q^2\) is obtained. Which conclusion follows correctly?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich of the following number-theoretic facts is used centrally in proving that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn a proof by contradiction, suppose \(\sqrt{2}=\frac{h}{k}\), where \(h\) and \(k\) are coprime integers. Which conclusion contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich of the following statements is essential in a proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. After obtaining \(3q^2=p^2\), which of the following conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn a proof by contradiction that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. Which conclusion from \(p^2=3q^2\) is needed to establish the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich property of the prime number 3 is used decisively in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which statement correctly justifies the conclusion \(3\mid p\) from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn proving the irrationality of ext{\(\sqrt{3}\)} , Ravi assumes that ext{\(\sqrt{3}=p/q\)} , where ext{\(p\)} and ext{\(q\)} are coprime. From ext{\(p^2=3q^2\)} , he says that only ext{\(p\)} is divisible by 3 and nothing can be concluded about ext{\(q\)} . Which fact corrects his error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion follows from this assumption and contradicts the fraction being in lowest terms?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich of the following numbers can be proved irrational using its prime factorisation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion about \(p\) and \(q\) contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion establishes the contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student assumes \(\sqrt{2}=p/q\), where \(p\) and \(q\) are coprime integers, to prove that \(\sqrt{2}\) is irrational. From \(p^2=2q^2\), the student writes \(p=2m\) and obtains \(q^2=2m^2\). The student says that since \(p\) and \(q\) are coprime, \(q\) must be odd. What is the correct correction to this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn the contradiction proof of the irrationality of \(\sqrt{3}\), we assume \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. If both \(p\) and \(q\) are finally found to be divisible by 3, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIn the proof by contradiction for the irrationality of sqrt(3), before assuming sqrt(3) = p/q, which condition is essential for the fraction p/q?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert 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