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Square Root 3

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

MathematicsWhat is the final contradiction in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium MathematicsIf assuming √3 is rational breaks the coprime condition, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium 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 3Medium 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 3Medium 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 3Medium MathematicsWhich option shows the correct logical chain in the proof of (√3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhich statement is a wrong conclusion in the proof of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium 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 3Medium 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 3Medium 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 3Medium 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 3Medium 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 3Medium MathematicsWhich option gives the correct conclusion and reason for the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium 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 3Medium 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 3Medium 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 3Medium