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 \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which correct conclusion follows from this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, \(a^2=3b^2\) gives \(3\mid a^2\). Which rule justifies the next step?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. After concluding from \(p^2=3q^2\) that \(p\) is divisible by 3, which conclusion completes the contradiction proving \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn a proof by contradiction that \(\sqrt{3}\) is irrational, what fact produces the contradiction after assuming \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime integers?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf sqrt{2} is an irrational number, which of the following numbers must also be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says, “3 is a rational number, so \(\sqrt{3}\) must also be rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsBefore assuming \(\sqrt{3}=\frac{p}{q}\) in a proof by contradiction that \(\sqrt{3}\) is irrational, which condition on \(p\) and \(q\) is essential?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRima says that \(5+\sqrt{2}\) is a rational number because 5 is rational. Which is the correct evaluation of her statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRiya assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, she gets \(p^2=3q^2\). Which argument correctly proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn which of the following options are both numbers irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(4+\sqrt{3}\) is a rational number because 4 is rational. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsReema says that \(\sqrt{3}\) is rational because 3 is a rational number. What is her error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsSuppose \\(\sqrt{3}=\frac{p}{q}\\), where p and q are coprime positive integers. In the proof that \\(\sqrt{3}\\) is irrational, which fact gives the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich statement is correct about \(\sqrt{2}\) and \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(2\sqrt{3}\) is rational because 2 is a rational number. What is the error in the student's statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that \(\sqrt{3}\) is rational because \(1.7^2=2.89\), which is very close to 3. What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that \(2\sqrt{2}\) is rational because 2 is a rational number. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=p/q\) where \(p\) and \(q\) are coprime, which conclusion is essential to the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhat is the main purpose of assuming \(\frac{p}{q}\) is in lowest terms in the contradiction proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsRiya assumes that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. If the proof shows that both \(a\) and \(b\) are divisible by 3, what conclusion follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy