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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।

MathematicsRiya claims that the product of any two irrational numbers is always irrational. Which of the following pairs is a counterexample to her claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is the value of (√8 + √18)(√8 − √18)?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhich of the following decimal representations denotes an irrational number?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is the square of \(\sqrt{2+\sqrt{3}}\) equal to?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is the value of (\frac{\sqrt{45}-\sqrt{20}}{\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsLet p and q be rational numbers with q ≠ 0. If a student claims that \(\frac{p+\sqrt{2}}{q}\) is rational, which conclusion would follow from the claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhich number definitely lies between (\sqrt{6}) and (\sqrt{7})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student claims that \(\frac{1}{\sqrt{5}+2}\) is a rational number because its numerator is 1. Which is the correct evaluation of this claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf \(x\) is an irrational number, which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsRiya says that \(\sqrt{45}+\sqrt{5}=\sqrt{50}\). Which is the correct evaluation of her statement?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is the value of 1/(√3 + √2) + 1/(√3 − √2)?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhat is the simplified form of (\sqrt{200}-\sqrt{128}+\sqrt{18})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf a rectangle has length (3+\sqrt{2}) and breadth (3-\sqrt{2}), what will be its area?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsRiya claims, “The square of every irrational number is also irrational.” Which of the following examples disproves her claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIn which option is the result not rational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student claims that the product of two non-zero irrational numbers is always irrational. Which of the following pairs provides a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhich is the simplified form of (\frac{\sqrt{3}-1}{\sqrt{3}+1})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf (s=\sqrt{27}+\sqrt{12}), what is the value of (\frac{s}{\sqrt{3}})?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions must be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard