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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।

MathematicsLet \(p\) be a rational number and \(x\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich number definitely lies between (\sqrt{18}) and (\sqrt{20})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(a\) be a non-zero rational number and \(b\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the rationalised form of 3/(√17 + √8)?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsWhich of the following statements is necessarily true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of \(\sqrt{7}\left(\sqrt{175}-\sqrt{63}\right)\)?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 MathematicsWhich is the simplified form of (\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf y = √27 + √75, what is the value of y/√3?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsLet \(x\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf a rectangle has length (\sqrt{22}+\sqrt{7}) and breadth (\sqrt{22}-\sqrt{7}), what will be its area?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the square of \(\sqrt{13+\sqrt{42}}\) equal to?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that every non-terminating decimal is irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the rationalised form of (\frac{6}{\sqrt{19}-\sqrt{10}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the simplified form of (\sqrt{539}-\sqrt{275}+\sqrt{99})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(x\) be an irrational number and \(q\) be a non-zero rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of (\frac{\sqrt{98}-\sqrt{50}}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf (t=\sqrt{23}+4), what is the value of (t+\frac{7}{t})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following numbers is rational despite containing square-root signs?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following decimal expansions identifies a real number as irrational?Class 9Number SystemsIrrational numbersLevel 14Expert