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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।

MathematicsWhat is the rationalised form of (\frac{9}{\sqrt{26}+\sqrt{17}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf (P=\sqrt{363}+\sqrt{147}-\sqrt{75}), what is (P) equal to?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(r\) is a non-zero rational number and \(x\) is an irrational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that \(5+\sqrt{7}\) is rational because it is the sum of two real numbers. Which argument proves the claim wrong?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(r\) be a rational number. Which statement about \(r+\sqrt{2}\) is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsRina says in class that the sum of two irrational numbers is always irrational. Which of the following examples disproves her statement?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the simplified form of (\sqrt{242}-\sqrt{128}+\sqrt{72})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsReema claims that for any rational number \(r\), \(r+\sqrt{7}\) will be irrational. Which of the following arguments correctly evaluates her claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the rationalised form of (\frac{5}{\sqrt{29}+2})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsRiya claims that \(0.101001000100001\ldots\) is rational because only the digits 0 and 1 occur in it. Which is the correct refutation of her claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following expressions represents an irrational number?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of ((\sqrt{44}+\sqrt{99})^2)?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf (P=\sqrt{363}+\sqrt{108}-\sqrt{192}), what is (P) equal to?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich is the rationalised form of (\frac{8}{\sqrt{18}-\sqrt{10}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf (r=\sqrt{13}+\sqrt{7}) and (s=\sqrt{13}-\sqrt{7}), what is the value of (r^2-s^2)?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of (\frac{\sqrt{200}+\sqrt{72}}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf r is an irrational number and q is a rational number, which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the value of (\frac{1}{\sqrt{7}+\sqrt{5}}+\frac{1}{\sqrt{7}-\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhat is the simplified form of (\sqrt{432}-\sqrt{192}+\sqrt{48})?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(r\) is a rational number and \(x\) is an irrational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert