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Number Systems

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

MathematicsWhat is the correct difference between the roles of (q\neq0) and (\gcd(p,q)=1) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhat is the correct difference between the roles of (b\neq0) and (\gcd(a,b)=1) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhat is the main purpose of assuming \(\sqrt{2}=\frac{p}{q}\) in lowest terms in the standard proof by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsRima says that \(\sqrt{3}\) is irrational because its decimal expansion continues infinitely. What is the main flaw in her argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf (p) is not divisible by (3) in the proof of (\sqrt{3}), what contradiction follows from (p^2=3q^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIn a proof by contradiction for the irrationality of \(\sqrt{3}\), which conclusion is necessary to proceed after obtaining \(a^2=3b^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhich statement about exponents of prime factors in perfect squares is useful in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsWhich statement about exponents of prime factors in perfect squares connects to the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsHow can the proof of (\sqrt{3}) be understood in the language of infinite descent?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of √2, the idea of infinite descent is connected with which situation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIf someone writes (p=3q) from (p^2=3q^2), what is the correct correction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIf someone writes (a=2b) from (a^2=2b^2), what is the correct correction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student assumes \(\sqrt{2}=\frac{m}{n}\), where \(m,n\) are integers, to prove that \(\sqrt{2}\) is irrational. Later, the student finds that both \(m\) and \(n\) are even and calls this a contradiction. Which essential condition is missing from the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert 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 MathematicsFor a positive integer \(n\), which condition identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert 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 MathematicsWhy is only (p) being divisible by (3) not the final contradiction in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert 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 MathematicsA student claims that \(1+\sqrt{2}\) is rational because 1 is a rational number. Which argument correctly refutes the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert 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