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

Coprime Integers

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

MathematicsA student assumes \(\sqrt{2}=\frac{m}{n}\), where \(m,n\) are integers, to prove that \(\sqrt{2}\) is irrational. Later, the student finds that both \(m\) and \(n\) are even and calls this a contradiction. Which essential condition is missing from the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhile proving the irrationality of \(\sqrt{3}\), assume that \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. Which conclusion obtained from \(p^2=3q^2\) contradicts this assumption?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 integers. After obtaining \(p^2=3q^2\), the student says, “\(p\) is divisible by 3, but \(q\) need not be divisible by 3.” Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, assume that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion makes this assumption impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, where \(p\) and \(q\) are coprime integers, which statement produces the contradiction in the proof of its irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which contradiction follows from this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(p/q\) be taken in lowest terms in the standard proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(\sqrt{3}=\frac{p}{q}\) be assumed to be in lowest terms while proving 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 is the correct initial assumption for treating \(\sqrt{2}\) as rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. From \(a^2=2b^2\), the student concludes that both \(a\) and \(b\) are even. Which statement explains why this creates a contradiction?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 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 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 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 MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion is needed to establish the contradiction in the proof of irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf \(\sqrt{3}=p/q \), where \(p \) and \(q \) are coprime positive integers, which conclusion is required to establish the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, which conclusion necessarily follows from \(3q^2=p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=\frac{p}{q}\) is assumed, which condition on \(p\) and \(q\) is necessary?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard