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Irrational Numbers

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

MathematicsWhich is the simplified form of (\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhich of the following statements is always true about the sum of two irrational numbers?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the value of (√20 + √45)(√20 − √45)?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsIn which option is the difference of two irrational numbers rational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf \(p\) is an irrational number and \(q\) is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the square of \(\sqrt{7+\sqrt{10}}\) equal to?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the value of (\frac{\sqrt{125}-\sqrt{20}}{\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 14Hard 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 numbersLevel 14Hard MathematicsWhich number definitely lies between (\sqrt{10}) and (\sqrt{12})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsRavi claims that \(x=\frac{3+\sqrt{2}}{5}\) is rational because its denominator is 5. What is the error in Ravi’s claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIn which option are both numbers irrational, but their sum is rational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsReena claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs disproves her claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the value of (\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{5}-\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the simplified form of (\sqrt{300}-\sqrt{192}+\sqrt{75})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf a rectangle has length (4+\sqrt{5}) and breadth (4-\sqrt{5}), what will be its area?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsReema claims that the product of two irrational numbers is always irrational. Which of the following examples disproves her claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsFor a positive integer \(n\), which criterion correctly determines that \(\sqrt{n}\) is irrational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhich is the simplified form of (\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf (s=\sqrt{48}+\sqrt{75}), what is the value of (\frac{s}{\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf t = √7 + 2, what is the value of t + 3/t?Class 9Number SystemsIrrational numbersLevel 14Medium