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Square Root Of 3

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

MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), the student says, “\(p\) is divisible by 3, but \(q\) need not be divisible by 3.” Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion is needed to establish the contradiction in the proof of irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\) is in lowest terms. What conclusion about \(p\) follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf (p^2=3q^2) and (p=3k), what combined conclusion about (p) and (q) follows from (q^2=3k^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “\(\sqrt{3}=1.732\), so \(\sqrt{3}\) is a rational number.” What is the main error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf (r=3t) and (r^2=3s^2), what follows next?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy