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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 \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs is a counterexample to this claim?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich of the following statements correctly identifies the decimal expansion of an irrational number?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf y = √8 + √18, what is the value of y/√2?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsIf a rectangle has length (\sqrt{14}+\sqrt{5}) and breadth (\sqrt{14}-\sqrt{5}), what will be its area?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the square of \(\sqrt{10+\sqrt{21}}\) equal to?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich of the following statements is necessarily true for every irrational number \(x\)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (t=\sqrt{17}+4), what is the value of (t+\frac{1}{t})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number and \(r\) is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich decimal can be considered an example of an irrational number?Class 9Number SystemsDecimal representationLevel 13Medium MathematicsReema writes the number \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. Which conclusion about this number is correct?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number and \(r\) is a non-zero rational number, which statement about \(rx\) is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of (\sqrt{6+\sqrt{7}}\times\sqrt{6+\sqrt{7}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the rationalised form of (\frac{3}{\sqrt{7}+\sqrt{4}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student claims, “The sum of two irrational numbers is always irrational.” Which of the following examples proves this claim wrong?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich of the following numbers, based on its decimal expansion, is irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf r is a non-zero irrational number and q is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the simplified form of \(\sqrt{200}-\sqrt{72}+\sqrt{18}\)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student says, “Every number with a non-terminating decimal expansion is irrational.” Which of the following numbers proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich is the simplified form of (\frac{\sqrt{5}+2}{\sqrt{5}-2})?Class 9Number SystemsIrrational numbersLevel 13Expert