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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।

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 3Level 17Hard 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 3Level 16Hard MathematicsWhich of the following conclusions about radicals is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsFor a positive integer \(n\), which of the following statements is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard 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 3Level 18Medium 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 3Level 18Medium 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 3Level 17Medium 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 3Level 17Medium 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 3Level 17Medium MathematicsWhich of the following numbers has an irrational positive square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn which of the following options are both numbers irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich statement is correct about \(\sqrt{2}\) and \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium 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 3Level 21Easy MathematicsWhich of the following numbers has an irrational square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy 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 3Level 19Easy MathematicsWhich of the following examples shows that the product of two irrational numbers can be rational?Class 9Number SystemsIrrational numbersLevel 15Expert 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 numbersLevel 15Expert MathematicsA student claims, “The square of every irrational number is irrational.” Which example disproves this claim?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student claims that \(5+\sqrt{7}\) is rational because it is the sum of two real numbers. Which argument proves the claim wrong?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves this claim?Class 9Number SystemsIrrational numbersLevel 14Expert