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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।

MathematicsIn a proof by contradiction that \(\sqrt{3}\) is irrational, what fact produces the contradiction after assuming \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime integers?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says, “3 is a rational number, so \(\sqrt{3}\) must also be rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsBefore assuming \(\sqrt{3}=\frac{p}{q}\) in a proof by contradiction that \(\sqrt{3}\) is irrational, which condition on \(p\) and \(q\) is essential?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf √3 were rational, which statement about p/q should be correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of √3, after both p and q become divisible by 3, what is the final conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRiya assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, she gets \(p^2=3q^2\). Which argument correctly proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (p^2=3q^2) and (p=3k), why will (q) be divisible by (3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(4+\sqrt{3}\) is a rational number because 4 is rational. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsReema says that \(\sqrt{3}\) is rational because 3 is a rational number. What is her error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsSuppose \\(\sqrt{3}=\frac{p}{q}\\), where p and q are coprime positive integers. In the proof that \\(\sqrt{3}\\) is irrational, which fact gives the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(2\sqrt{3}\) is rational because 2 is a rational number. What is the error in the student's statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that \(\sqrt{3}\) is rational because \(1.7^2=2.89\), which is very close to 3. What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=p/q\) where \(p\) and \(q\) are coprime, which conclusion is essential to the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsRiya assumes that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. If the proof shows that both \(a\) and \(b\) are divisible by 3, what conclusion follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIn the proof of \(\sqrt{3}\), which conclusion is rejected by the rational assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. The student obtains \(p^2=3q^2\). Which conclusion from this step establishes the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy 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 3Level 21Easy MathematicsA student says that \(\sqrt{3}\) is rational because \(1.7^2=2.89\), which is very close to 3. What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsAman assumes that ext{\(\sqrt{3}=\frac{p}{q}\)}, where ext{\(p\)} and ext{\(q\)} are coprime. On squaring, he gets ext{\(p^2=3q^2\)}. Aman says, “ ext{\(3\mid p^2\)} does not necessarily imply ext{\(3\mid p\)}.” What is the correct evaluation of Aman’s statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(\sqrt{3}=\frac{p}{q}\) where \(p\) and \(q\) are coprime, which statement follows from \(p^2=3q^2\) and creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy