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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 of the following statements about decimal expansions is correct?Class 9Number SystemsReal NumbersLevel 3MediumMathematicsA student says that \(0.101001000100001\ldots\) is a rational number because its decimal expansion contains only the digits 0 and 1. Which statement correctly explains the student's error?Class 9Number SystemsReal NumbersLevel 3MediumMathematicsRavi says that \(\frac{7}{24}\) is an irrational number because its decimal expansion is non-terminating. What is the error in Ravi's statement?Class 9Number SystemsReal NumbersLevel 3MediumMathematicsA student writes: \(\sqrt{2}+\sqrt{8}=\sqrt{10}\). Which is the correct evaluation of this statement?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsWhat type of number is \(\sqrt{3}\times\sqrt{21}\)?Class 9Number SystemsIrrational numbersLevel 2MediumMathematicsA student considers the number \(0.101001000100001\ldots\) rational because its decimal expansion does not terminate. What is the correct conclusion about this number?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsA student calls the number \(0.101001000100001\ldots\) rational because it contains only the digits 0 and 1. Which conclusion about this number is correct?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsA square has a side length of 5 cm. What type of number is the length of its diagonal?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsA square tile has a side length of 1 cm. According to the Pythagorean theorem, its diagonal is \(\sqrt{2}\) cm. Which statement about this length is correct?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsIf 0.2020020002... has no fixed repetition, what type of number is it?Class 9Number SystemsExponentsLevel 3MediumMathematicsWhat is the rationalised form of \(\frac{6}{\sqrt{7}}\)?Class 9Number SystemsIrrational numbersLevel 2MediumMathematicsA student simplifies \\(\sqrt{50}\\) as \\(5\sqrt{2}\\) and calls it an irrational number. Which evaluation of the student's conclusion is correct?Class 9Number SystemsReal NumbersLevel 2MediumMathematicsA student calls the number 0.101001000100001... rational because its decimal expansion is infinite. What should the correct conclusion be?Class 9Number SystemsReal NumbersLevel 1MediumMathematicsA student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which statement correctly explains the student's error?Class 9Number SystemsReal NumbersLevel 1MediumMathematicsWhat type of number is \(\sqrt{7}\times\sqrt{14}\)?Class 9Number SystemsIrrational numbersLevel 1MediumMathematicsWhat type of number is √2 + √3?Class 9Number SystemsIrrational numbersLevel 2HardMathematicsA student says, “\(\sqrt{18}\) is a rational number because 18 is an integer.” Which is the correct evaluation of this statement?Class 9Number SystemsReal NumbersLevel 1MediumMathematicsA square has a side of \(\sqrt{2}\) cm. Which statement about its diagonal and perimeter is correct?Class 9Number SystemsReal NumbersLevel 1MediumMathematicsIf 0.040040004... has no fixed repetition, what is it?Class 9Number SystemsIrrational numbersLevel 1MediumMathematicsIf 0.12122122212222... is non-repeating, what type of number is it?Class 9Number SystemsIrrational numbersLevel 3Medium

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