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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।

MathematicsWhile proving the irrationality of \(\sqrt{3}\), assume that \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. Which conclusion obtained from \(p^2=3q^2\) contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the contradiction proof that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\), where \(\gcd(p,q)=1\). This gives \(p^2=3q^2\). Which principle is correctly applied from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsAssume that a/b is in lowest terms and obtain a² = 3b². Which conclusion about a is essential in the proof that √3 is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof by contradiction for the irrationality of \(\sqrt{3}\), why are \(p\) and \(q\) chosen to be coprime when assuming \(\sqrt{3}=\frac{p}{q}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhich statement is correct about the decimal expansion of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, where \(p\) and \(q\) are coprime integers, which statement produces the contradiction in the proof of its irrationality?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 property is used to infer \(3\mid p\) from \(3\mid p^2\) in the proof?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 contradiction follows from this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(p/q\) be taken in lowest terms in the standard proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich divisibility rule is crucial in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(\sqrt{3}=\frac{p}{q}\) be assumed to be in lowest terms while proving the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsChoose the correct order in the proof of √3.Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf p is not divisible by 3 in p² = 3q², what contradiction appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student assumes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, and obtains \(p^2=3q^2\). The student shows only that \(3\mid p\) and declares a contradiction. Which step correctly completes the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich property is used decisively in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, and obtains \(p^2=3q^2\). Which next step is logically valid for reaching a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes that \(\sqrt{3}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. During the proof, if both \(m\) and \(n\) are shown to be divisible by 3, what is the error in the student's assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student says, “Since 1.732 is a terminating decimal, \(\sqrt{3}\) is rational.” Which option correctly identifies the error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student claims that \(5+\sqrt{3}\) is a rational number. Which argument correctly disproves the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich assumption is made at the beginning to prove the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert