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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 (P=\sqrt{500}+\sqrt{180}-\sqrt{320}), what is (P) equal to?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student claims, “The square of every irrational number is irrational.” Which example disproves this claim?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf (r=\sqrt{17}+\sqrt{11}) and (s=\sqrt{17}-\sqrt{11}), what is the value of (r^2-s^2)?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the value of (\frac{\sqrt{392}+\sqrt{200}}{\sqrt{2}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsLet \(a\) be a rational number and \(b\) be an irrational number. Which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the value of (\frac{1}{\sqrt{10}+\sqrt{6}}+\frac{1}{\sqrt{10}-\sqrt{6}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the simplified form of (\sqrt{588}-\sqrt{300}+\sqrt{192})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student claims that \(5-\sqrt{7}\) is rational because 5 is rational and \(\sqrt{7}\) is a number. What is the error in the student's reasoning?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsReena states: “\(\sqrt{12}+\sqrt{27}\) is irrational because the sum of two irrational numbers is always irrational.” What is the correct evaluation of her statement?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student claims that every non-terminating decimal expansion is irrational. Which of the following numbers is a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich number definitely lies between (\sqrt{26}) and (\sqrt{30})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf p and q are irrational numbers and \(p+q\) is rational, which of the following expressions must be irrational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the rationalised form of (\frac{5}{\sqrt{26}+\sqrt{17}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student calls the number 0.101001000100001… rational because it contains only the digits 0 and 1. Why is the student’s conclusion incorrect?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the value of \(\sqrt{11}\left(\sqrt{539}-\sqrt{275}\right)\)?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsRiya says, “The square of every irrational number is also irrational.” Which of the following examples proves her statement wrong?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich is the simplified form of (\frac{\sqrt{10}-\sqrt{6}}{\sqrt{10}+\sqrt{6}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf y = √75 + √147, what is the value of y/√3?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student claims that the sum of any two irrational numbers is always irrational. Which of the following examples disproves this claim?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf a rectangle has length (\sqrt{30}+\sqrt{11}) and breadth (\sqrt{30}-\sqrt{11}), what will be its area?Class 9Number SystemsIrrational numbersLevel 15Expert