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Coprime Integers

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 \(\sqrt{3}=p/q\) 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 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 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 MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. Which conclusion produces a contradiction to this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf \(\sqrt{3}\) is assumed to be rational and written as \(\frac{p}{q}\), which condition is necessary for \(p\) and \(q\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhile proving that \(\sqrt{2}\) is irrational by contradiction, assume \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. After obtaining \(p^2=2q^2\) and showing that \(p\) is even, which conclusion must be established to get a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf a number can be written in the form \(\frac{p}{q}\), where \(p\) and \(q\) are coprime integers and \(q\neq 0\), what is it called?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring both sides, \(3q^2=p^2\) is obtained. Which conclusion proves the assumption wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then from \(p^2=2q^2\) only \(p\) is even and nothing can be said about \(q\). What is the student's error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then even if \(p\) is divisible by 3, \(q\) need not be divisible by 3. Why is the statement incorrect?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{2}\) is assumed to be \(\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, which conclusion creates the contradiction in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), which conclusion proves this assumption contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed, where \(p\) and \(q\) are coprime, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student assumes dfrac{p}{q} is in lowest terms and obtains p^2=3q^2 , where p and q are coprime. Which conclusion proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{3}=\frac{m}{n}\) is assumed, where \(m\) and \(n\) are coprime integers, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then when \(p\) is divisible by 3, \(q\) will also be divisible by 3. What conclusion does this statement lead to?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIn the proof by contradiction that \(\sqrt{2}\) is irrational, if \(\sqrt{2}=\frac{p}{q}\) is assumed where \(p,q\) are coprime, which conclusion creates a contradiction with the initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy