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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।

MathematicsA student claims that the sum of any two irrational numbers is always irrational. Which of the following examples proves the claim wrong?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims that the sum of two irrational numbers is always irrational. Which of the following expressions is a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of (\frac{1}{\sqrt{8}+\sqrt{6}}+\frac{1}{\sqrt{8}-\sqrt{6}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the simplified form of (\sqrt{500}-\sqrt{320}+\sqrt{180})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf a rectangle has length (5+\sqrt{11}) and breadth (5-\sqrt{11}), what will be its area?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich of the following options contains only irrational numbers?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student has written the following conclusions about irrational numbers. Which conclusion is always correct?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich is the simplified form of (\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf (s=\sqrt{75}+\sqrt{192}), what is the value of (\frac{s}{\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf (t=\sqrt{13}+3), what is the value of (t+\frac{4}{t})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich is the simplified form of (\sqrt{242}+\sqrt{128}-\sqrt{72})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of (√(6 + √5) × √(6 + √5))?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhich of the following statements correctly describes the relationship between rational and irrational numbers?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the rationalised form of (\frac{5}{\sqrt{12}+\sqrt{7}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of \(\sqrt{5}\left(\sqrt{125}-\sqrt{45}\right)\)?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich condition on two irrational numbers guarantees that their sum is rational?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of ((\sqrt{50}+\sqrt{98})^2)?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich is the rationalised form of (\frac{6}{\sqrt{15}-\sqrt{6}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf \(x\) is an irrational number and \(r\ne 0\) is a rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich statement is definitely true about (\sqrt{10+\sqrt{21}})?Class 9Number SystemsIrrational numbersLevel 15Hard