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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।

MathematicsIf \(a\) is an irrational number and \(b\) is a non-zero rational number, which statement about \(a+b\) is always true?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf (x=\sqrt{8}+\sqrt{3}) and (y=\sqrt{8}-\sqrt{3}), what is the value of (\frac{x}{y})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the simplified form of (\frac{\sqrt{5}+2}{\sqrt{5}-2})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf two irrational numbers \(a\) and \(b\) are such that \(a+b\) is rational, which conclusion about \(ab\) is correct?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of (\sqrt{9+\sqrt{20}}\times\sqrt{9+\sqrt{20}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf (p=\frac{1}{\sqrt{13}+3}), which is the simplified form of (p)?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is (\sqrt{147}-\sqrt{75}+\sqrt{27}) equal to?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student says that every non-terminating decimal number is irrational. Which of the following numbers shows the error in this statement?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich is the simplified form of (\frac{4+\sqrt{7}}{4-\sqrt{7}})?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs disproves this claim?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhat is the value of (√45 + √5)(√45 − √5)?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsWhich conclusion about the side of a square tile with an area of 50 cm² is correct?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhich option will remain irrational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf a = √3 + √5 and b = √5 − √3, what is the value of ab?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsIf (s=\sqrt{98}+\sqrt{200}), what is the value of (\frac{s}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the rationalised form of (\frac{2}{\sqrt{11}+\sqrt{7}})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhat is the value of ((\sqrt{18}+\sqrt{50})^2)?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf r = 1/(√11 + 3), which is the simplified form of r?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsWhat is the simplified form of (\sqrt{245}-\sqrt{180}+\sqrt{80})?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsA student claims that \(5-\sqrt{7}\) is a rational number. Which argument correctly proves that the claim is wrong?Class 9Number SystemsIrrational numbersLevel 14Hard