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।

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 assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, the student gets \(p^2=2q^2\). Which of the following is the valid next inference?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 MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion creates the contradiction in the proof by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert 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 MathematicsA student claims that if \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=2q^2\) implies only that \(p\) is even; nothing can be concluded about \(q\). What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert 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 of the following integers has a rational square root?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 claims that \(\sqrt{2}+\sqrt{3}\) is a rational number. Which argument correctly identifies the error in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert 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, 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 MathematicsWhy must the fraction be taken in lowest terms when assuming \(\sqrt{2}=\frac{p}{q}\) in the proof that \(\sqrt{2}\) is irrational?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 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