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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 expressions can be rational for an irrational number \(x\)?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student examines the number \(x=0.101001000100001\ldots\) and draws a conclusion about its type. Which of the following conclusions is correct?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf x = 1/(√2 + 1), what is the value of x + √2?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsIf m = √8 + √18 and n = √50, what is the value of m − n?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsHow can (\sqrt{3+\sqrt{5}}) be identified according to the given statements?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student claims that the sum of two irrational numbers is always irrational. Which example shows the error in this claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is (\sqrt{45}+\sqrt{20}-\sqrt{80}) equal to?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf \(x\) is an irrational number, which of the following numbers will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhich is the simplified form of (\frac{2+\sqrt{3}}{2-\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says, “The sum of two irrational numbers can never be rational.” Which of the following pairs proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says that the decimal number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly identifies the student's error?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhich of the following numbers has a decimal expansion that indicates it is an irrational number?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhat is the simplified value of (\frac{\sqrt{98}-\sqrt{18}}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhich is irrational between (0.414141\ldots) and (0.4141141114\ldots)?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsIf a = √8 − √2, what is a equal to?Class 9Number SystemsIrrational numbersLevel 15Easy MathematicsWhich is the rationalised form of (\frac{4}{\sqrt{3}+1})?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsRina says, “\(\sqrt{18}\) is rational because 18 is an integer.” Which option correctly identifies her error?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsIf x = √12 + 2√3, what is the simplified form of x?Class 9Number SystemsIrrational numbersLevel 15Easy MathematicsA student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. Which statement correctly corrects the student's claim?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student claims that every non-terminating decimal number is irrational. Which of the following numbers is a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 15Medium