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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।

MathematicsSuppose \(x\) is an irrational number and \(q\) is a non-zero rational number. Which statement about \(qx\) is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number, which of the following expressions is not necessarily irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of (\frac{\sqrt{45}+\sqrt{80}}{\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf u = 3√2 + √98 − √50, what is the value of u/√2?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsIf a rectangle has length √18 + √2 and breadth √18 − √2, what will be its area?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsIf (y=\sqrt{14}-\sqrt{7}), which is the simplified value of (y^2)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the rationalised form of (\frac{5}{\sqrt{17}+\sqrt{8}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of (√18 + √50)/√8?Class 9Number SystemsIrrational numbersLevel 13Medium MathematicsIf \(x\) is an irrational number, which of the following expressions will be irrational in every case?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions is always irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of ((\sqrt{28}+\sqrt{63})^2)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (P=\sqrt{242}+\sqrt{50}-\sqrt{98}), what is (P) equal to?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf (r=\sqrt{7}+\sqrt{2}) and (s=\sqrt{7}-\sqrt{2}), what is the value of (r^2-s^2)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the value of (\frac{\sqrt{72}+\sqrt{128}}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(x\) be an irrational number and \(r\) be a non-zero rational number. Which of the following expressions must be irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhat is the simplified form of (\sqrt{300}-\sqrt{108}+\sqrt{75})?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(a\) and \(b\) be rational numbers, \(b\ne0\), and let \(m\) be a natural number that is not a perfect square. What type of number is \(a+b\sqrt{m}\)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student says, “The product of two irrational numbers is always irrational.” Which example disproves this statement?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich number definitely lies between (\sqrt{7}) and (\sqrt{8})?Class 9Number SystemsIrrational numbersLevel 13Expert