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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।

MathematicsA student claims, “The square of every irrational number is irrational.” Which example disproves this claim?Class 9Number SystemsIrrational numbersExpert 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 numbersExpert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves this claim?Class 9Number SystemsIrrational numbersExpert MathematicsWhich of the following numbers is rational despite containing square-root signs?Class 9Number SystemsIrrational numbersExpert MathematicsWhere \(q\) is any rational number, which of the following expressions is guaranteed to be irrational?Class 9Number SystemsIrrational numbersExpert MathematicsRiya states, “The product of two irrational numbers is always irrational.” Which of the following examples disproves her statement?Class 9Number SystemsIrrational numbersExpert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersExpert MathematicsA student says, “The product of two irrational numbers is always irrational.” Which example disproves this statement?Class 9Number SystemsIrrational numbersExpert MathematicsA student says that \(\sqrt{12}-\sqrt{3}\) is the difference of two square roots, so it is a rational number. Which is the correct correction of the student's error?Class 9Number SystemsIrrational numbersHard MathematicsRiya says that the quotient of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?Class 9Number SystemsIrrational numbersHard MathematicsA student says, “The product of two irrational numbers is always irrational.” Which of the following examples proves this statement wrong?Class 9Number SystemsIrrational numbersHard MathematicsWhich of the following options contains only irrational numbers?Class 9Number SystemsIrrational numbersHard MathematicsWhich conclusion about the side of a square tile with an area of 50 cm² is correct?Class 9Number SystemsIrrational numbersHard MathematicsA student claims that \(5-\sqrt{7}\) is a rational number. Which argument correctly proves that the claim is wrong?Class 9Number SystemsIrrational numbersHard MathematicsIn which option is the difference of two irrational numbers rational?Class 9Number SystemsIrrational numbersHard MathematicsA student claims that \(\frac{\sqrt{18}}{\sqrt{2}}\) must be irrational because both the numerator and denominator are irrational. What is the correct conclusion?Class 9Number SystemsIrrational numbersHard MathematicsReema claims that the product of two irrational numbers is always irrational. Which of the following examples disproves her claim?Class 9Number SystemsIrrational numbersHard MathematicsFor a positive integer \(n\), which criterion correctly determines that \(\sqrt{n}\) is irrational?Class 9Number SystemsIrrational numbersHard MathematicsWhat is the value of √(4 + √7) × √(4 + √7)?Class 9Number SystemsIrrational numbersEasy MathematicsA student claims that the quotient of any two irrational numbers is always irrational. Which of the following calculations conclusively proves the claim wrong?Class 9Number SystemsIrrational numbersHard