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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।

MathematicsWhich statement correctly describes the main idea used in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsOn what basis does the final conclusion in irrationality of (√2) come?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn a proof by contradiction, Arjun assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. He obtains \(m^2=2n^2\) and says, “\(m\) is even, so \(\sqrt{2}\) is irrational.” What is missing from his argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option shows the correct logical chain in the proof of (√2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=2q^2\), which conclusion creates a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that if the square of an integer is divisible by 2, then the integer itself is divisible by 2. How is this statement useful in proving the irrationality of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhy is \(\frac{p}{q}\) taken in lowest terms while proving the irrationality of \(\sqrt{2}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of √2, what is finally proved false?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf sqrt{2} is an irrational number, which of the following numbers must also be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRima says that \(5+\sqrt{2}\) is a rational number because 5 is rational. Which is the correct evaluation of her statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (a^2=2b^2) and (a=2r), why will (b) be even?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that \(2\sqrt{2}\) is rational because 2 is a rational number. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhat is the main purpose of assuming \(\frac{p}{q}\) is in lowest terms in the contradiction proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsRiya says that since a calculator displays \(\sqrt{2}\) as 1.414, \(\sqrt{2}\) is a rational number. What is the error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says, “If n is an integer, then \(\sqrt{n}\) will also be an integer.” Which example is most suitable to disprove this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf \(\sqrt{2}\) is assumed to be \(\frac{p}{q}\) in lowest terms, which conclusion creates the contradiction in proving that it is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhile proving the irrationality of \(\sqrt{2}\), a student assumes \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. On obtaining \(p^2=2q^2\), the student immediately says that \(q\) is even. How should the teacher correct the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf (m=2k) and (m^2=2n^2), which relation follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhich statement creates a contradiction in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsRiya says, “Since 2 is an integer, \(\sqrt{2}\) must also be a rational number.” What is Riya’s error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy