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Class 9 Mathematics

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

MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms and \(p^2=3q^2\) is obtained, which conclusion is necessary to reach the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, Riya shows that in the fraction \(a/b\) written in lowest terms, both \(a\) and \(b\) are divisible by 3. Why is this conclusion impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsA student claims that \(\sqrt{12}\) is rational because 12 is not a perfect square. Which is the correct simplified form of \(\sqrt{12}\) that identifies the error in the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsA student assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. Which conclusion from \(m^2=2n^2\) proves that this assumption is contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, which conclusion about \(p\) and \(q\) produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsFor a positive integer \(n\), which statement correctly identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion is necessary to establish the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms to prove irrationality, which statement establishes the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard 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 3Hard 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 3Medium 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 3Medium MathematicsWhich of the following decimal expansions indicates an irrational number?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium MathematicsWhich of the following numbers cannot be written as a ratio \(p/q\) of two integers, where \(q\ne0\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsA student claims that \(\sqrt{3}\) is rational because its square, \(3\), is a rational number. Which statement about this argument is correct?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 MathematicsIn which of the following options are both numbers irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhich statement is correct about \(\sqrt{2}\) and \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsA student says, “1.732 is a terminating decimal and is very close to \(\sqrt{3}\), so \(\sqrt{3}\) is rational.” What is the main error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsA student claims that √12 is irrational because √12 = 2√3. Which statement is needed to make this argument valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy