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Irrational Numbers

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (a) and (b) are positive integers and (\sqrt{a}+\sqrt{b}) is rational, while (a) is not a perfect square, which conclusion about (b) can definitely be true?Class 10Real NumbersIrrational numbersLevel 13Expert MathematicsIf (A=(3+\sqrt{2})^2-(3-\sqrt{2})^2), what is the correct value and nature of (A)?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsIf (m) is a positive integer and (m) is not a perfect square, which statement about (\sqrt{m}+4) is correct?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich number lies between (\sqrt{3}) and (2\sqrt{3})?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsIf (x=\sqrt{7}), what is the nature of (3x-2)?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsIf (x=2-\sqrt{3}), what is the rationalized form of (\frac{1}{x})?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich option is the correct simplified form of (\sqrt{5}+\sqrt{45}-\sqrt{20})?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich option is the correct simplified form of (\sqrt{98}-\sqrt{50})?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsIf (\sqrt{n}) is rational when (n) is a positive integer, what is the correct decision for (n=72)?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich of the following decimals represents an irrational number?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich option gives the correct simplified form and nature of (\sqrt{2}+\sqrt{18})?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsIf (r) is a non-zero rational number and (x) is an irrational number, which statement about (\frac{x}{r}) is correct?Class 10Real NumbersIrrational numbersLevel 15Hard MathematicsWhich option gives a rational decimal even though it does not terminate?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsIf (x=\sqrt{11}+\sqrt{44}), what is the simplified form and nature of (x)?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsWhich option gives the correct simplified form and nature of (\sqrt{32}-\sqrt{2})?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsIf (a) is irrational and (b) is irrational, which conclusion is not always correct?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsIn which option is the number definitely irrational?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsWhich statement is correct for (\sqrt{12})?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsWhich option is equal to (2\sqrt{6})?Class 10Real NumbersIrrational numbersLevel 14Hard MathematicsIf (2+\sqrt{7}) is assumed rational, which conclusion creates a contradiction?Class 10Real NumbersIrrational numbersLevel 14Hard