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Square Roots

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

MathematicsRima says, “If \(\sqrt{12}\) were rational, then \(\sqrt{3}=\frac{\sqrt{12}}{2}\) would also be rational, which contradicts the irrationality of \(\sqrt{3}\).” What is Rima’s conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsA student says that \(\sqrt{2}+\sqrt{3}\) is irrational because the sum of two irrational numbers is always irrational. What is the correct evaluation of this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsA student claims that \(\sqrt{12}\) is rational because 12 is not a perfect square. Which is the correct simplified form of \(\sqrt{12}\) that identifies the error in the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsFor a positive integer \(n\), which statement correctly identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsSuppose \(r=\sqrt{2}+\sqrt{3}\) is a rational number. Which conclusion from this assumption proves by contradiction that \(\sqrt{2}+\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsWhich of the following conclusions about radicals is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsFor a positive integer \(n\), which of the following statements is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsA student believes that any number with an infinite decimal expansion must be irrational. Which example disproves this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIt is known that \(\sqrt{3}\) is irrational. Which argument correctly completes a proof that \(\sqrt{12}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIf a prime number has an odd exponent in the prime factorisation of a number, what can be concluded about the square root of that number?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhich of the following numbers cannot be written as a ratio \(p/q\) of two integers, where \(q\ne0\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsA student claims that \(\sqrt{3}\) is rational because its square, \(3\), is a rational number. Which statement about this argument is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhich of the following numbers has an irrational positive square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIn which of the following options are both numbers irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhich statement is correct about \(\sqrt{2}\) and \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsA student claims that √12 is irrational because √12 = 2√3. Which statement is needed to make this argument valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsWhich of the following numbers has an irrational square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsWhich of the following correctly describes the nature of the number \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsWhich of the following examples shows that the product of two irrational numbers can be rational?Class 9Number SystemsIrrational numbersExpert MathematicsA student says, “The product of two irrational numbers is always irrational.” Which of the following examples proves that the statement is wrong?Class 9Number SystemsIrrational numbersExpert