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।

MathematicsSuppose \(\sqrt{3}=\frac{m}{n}\), where \(m\) and \(n\) are coprime integers. Which conclusion proves a contradiction to this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsRiya says, “ \(\sqrt{3}=1.732\ldots\), so it is irrational because its decimal expansion is non-terminating.” What is the main error in Riya’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option gives the correct squared relation used in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich statement correctly describes the main idea used in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student claims that \(\sqrt{3}\) is rational because its square, \(3\), is a rational number. Which statement about this argument is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf \(\sqrt{3}\) is assumed to be \(\frac{p}{q}\) in lowest terms, where \(p\) and \(q\) are coprime integers, what follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn a proof by contradiction, Arjun assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. He obtains \(m^2=2n^2\) and says, “\(m\) is even, so \(\sqrt{2}\) is irrational.” What is missing from his argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student says, “3 is not a perfect square, so \(\sqrt{3}\) is irrational.” Which step is needed to complete this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn a proof that √3 is irrational, suppose √3 = p/q, where p and q are coprime. Squaring gives p² = 3q², and on writing p = 3k, we get q² = 3k². Which conclusion is needed to complete the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich of the following numbers has an irrational positive square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. If \(p^2=3q^2\) is obtained, what is the correct next conclusion in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if assuming \(\sqrt{3}=\frac{p}{q}\) in lowest terms gives \(p^2=3q^2\), which conclusion creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student claims that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=3q^2\) proves only that \(p\) is divisible by 3. What is the correct improvement to the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student has to prove that \(1+\sqrt{3}\) is irrational. Which of the following arguments is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=2q^2\), which conclusion creates a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that if the square of an integer is divisible by 2, then the integer itself is divisible by 2. How is this statement useful in proving the irrationality of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf assuming \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime, leads to \(p^2=3q^2\), which conclusion creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhy is \(\frac{p}{q}\) taken in lowest terms while proving the irrationality of \(\sqrt{2}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student writes: If \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime, then \(a^2=3b^2\). The student concludes that 3 divides \(b\). What is the error in this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium