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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 two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following conditions about the decimal expansion of a real number definitely identifies it as irrational?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsA student says that \(0.1010010001\ldots\) is a rational number because it contains only the digits 0 and 1. Why is the student's statement incorrect?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following statements is not always true?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhat is the simplified form of √2 + √8 + √18?Class 9Number SystemsIrrational numbersLevel 1Medium MathematicsIf 0.01001000100001... is non-terminating and non-repeating, what type of number is it?Class 9Number SystemsIrrational numbersLevel 1Medium MathematicsIf the decimal expansion of a real number is non-terminating and non-recurring, what type of number is it?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following numbers is irrational because its decimal expansion is non-terminating and non-repeating?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsIf \(x\) is an irrational number, which of the following statements is always true?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following numbers is definitely irrational?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsA student says, “A number with an infinite decimal expansion is always irrational.” Which of the following examples proves that the student's statement is incorrect?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsRiya says that the sum of any two irrational numbers is always irrational. Which of the following examples disproves her statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that the number 0.101001000100001... is rational because 0 occurs repeatedly in it. Which option is correct about this statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsWhich of the following numbers has a non-terminating, non-repeating decimal expansion?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsIf 0.3030030003... has no fixed repetition, what type of number is it?Class 9Number SystemsExponentsLevel 3Medium MathematicsA student says that the sum of two irrational numbers is always irrational. Which of the following examples disproves the statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that the decimal expansion of every irrational number is non-terminating and recurring. Why is this statement incorrect?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsWhich of the following numbers has a non-terminating, non-repeating decimal expansion and is therefore irrational?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsWhat is the rationalised form of ?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that \(\sqrt{2}+\sqrt{8}\) is an irrational number. Why is the statement correct?Class 9Number SystemsReal NumbersLevel 3Medium