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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।

MathematicsA calculator displays \(\sqrt{3}\) as 1.7320508. Which conclusion is correct based on this display?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option shows the correct cause-effect relation used in the proof of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed, where \(p\) and \(q\) are coprime integers, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that \(\sqrt{3}\) is irrational because its decimal expansion does not terminate. Which step correctly turns this into a rigorous proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich of the following statements is essential for proving the irrationality of \(\sqrt{3}\) by the contradiction method?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. What is the first conclusion obtained from \(3q^2=p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsRiya says that \(\sqrt{3}\) is rational because its decimal form is \(1.732\). Which statement correctly identifies the error in her claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student argues 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. Identify the student's error.Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, suppose \(\sqrt{3}=p/q\) is in lowest terms and squaring gives \(p^2=3q^2\). What correctly fixes a student's error that \(3\mid p^2\) does not imply \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsBefore proving the irrationality of \(\sqrt{3}\) by contradiction, in what form must \(\frac{p}{q}\) be assumed?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhile proving \(\sqrt{3}\) irrational by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. What follows immediately from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}\) is assumed to be \(\frac{p}{q}\) in lowest terms, what conclusion follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsSuppose a student writes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, while proving that \(\sqrt{3}\) is irrational. From \(p^2=3q^2\), which conclusion about \(p\) is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that since 5 is a rational number, \(5+\sqrt{3}\) must also be rational. Which statement correctly identifies the error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student believes that the statement “If the square of an integer is divisible by 3, then the integer is also divisible by 3” is false. Which statement correctly removes this misconception?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that sqrt3 is irrational, if sqrt3 = p/q is assumed to be in lowest terms, why does a contradiction arise?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich initial assumption is made to prove the irrationality of \(\sqrt{3}\) by the method of contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\) in lowest terms. If \(p\) is shown to be divisible by 3, which conclusion about \(q\) is needed to obtain a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, which statement produces the contradiction in the proof of its irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion produces a contradiction in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium