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Square Root 2

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

MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne0\), and concludes from \(p^2=2q^2\) that both \(p\) and \(q\) are even. If the student did not assume \(p\) and \(q\) to be coprime, why is this conclusion not automatically a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. On squaring, he gets \(p^2=2q^2\). He says that \(q\) is even because the right-hand side is even. What should be the first correct conclusion in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof by contradiction that \(\sqrt{2}\) is irrational, assume \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert 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 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 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 (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 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 MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, assume that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion makes this assumption impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIn a proof by contradiction that √2 is irrational, a student assumes √2 = a/b, where a and b are coprime positive integers. From 2b² = a², the student concludes that a is even. Which is the correct basis for this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsHow would the decimal expansion of \(\sqrt{2}\) be classified?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, and on squaring obtains \(p^2=2q^2\). Which reasoning correctly proves irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIf a student tries to prove irrationality of √2 by writing its decimal value, what is the correct evaluation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhat problem appears when a² = 2b² is viewed through prime factors in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA square has an area of \(2\text{ cm}^2\). A student says, “Since the area is rational, the side of the square must also be rational.” What is the correct correction to this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsChoose the correct order in the proof of √2.Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf (a) is assumed odd in (a^2=2b^2), what contradiction appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, which is the correct initial assumption for treating \(\sqrt{2}\) as rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. From \(a^2=2b^2\), the student concludes that both \(a\) and \(b\) are even. Which statement explains why this creates a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert