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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 is the simplified form of (\frac{\sqrt{13}+\sqrt{3}}{\sqrt{13}-\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsNidhi says that the number \(0.101001000100001\ldots\) is rational because its decimal expansion contains only 0 and 1. Which statement correctly explains Nidhi's error?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of (\sqrt{8+\sqrt{11}}\times\sqrt{8+\sqrt{11}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf s = √108 + √300, what is the value of s/√3?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsWhich is the rationalised form of (\frac{5}{\sqrt{14}-3})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(r\) be an irrational number and \(q\) be a non-zero rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(x\) is an irrational number and \(r\) is a rational number, which of the following expressions will be irrational in every case?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhere \(q\) is any rational number, which of the following expressions is guaranteed to be irrational?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich is the simplified form of (\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that \(3+\sqrt{2}\) is a rational number. Which argument proves the student's claim wrong?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the simplified value of (\frac{\sqrt{243}-\sqrt{108}}{\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (a=\sqrt{18}+\sqrt{8}) and (b=\sqrt{18}-\sqrt{8}), what is the value of (a^2-b^2)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of (\frac{1}{\sqrt{12}+\sqrt{5}}+\frac{1}{\sqrt{12}-\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsRiya states, “The product of two irrational numbers is always irrational.” Which of the following examples disproves her statement?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of ((\sqrt{32}+\sqrt{50})^2)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (t=\sqrt{19}+3), what is the value of (t+\frac{10}{t})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (P=\sqrt{363}-\sqrt{147}+\sqrt{75}), what is (P) equal to?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the rationalised form of (\frac{7}{\sqrt{19}-\sqrt{12}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(r\) is an irrational number and \(q\) is a rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the square of \(\sqrt{12+\sqrt{35}}\) equal to?Class 9Number SystemsIrrational numbersLevel 13Expert