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Number Systems

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(x\) is an irrational number, which of the following expressions will always be rational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich is the simplified form of (\frac{\sqrt{17}+\sqrt{5}}{\sqrt{17}-\sqrt{5}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich of the following decimal expansions definitely identifies the number as irrational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the value of (\sqrt{15+\sqrt{26}}\times\sqrt{15+\sqrt{26}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf s = √242 + √128, what is the value of s/√2?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhich is the rationalised form of (\frac{7}{\sqrt{30}-\sqrt{23}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf (y=\sqrt{20}+\sqrt{45}+\sqrt{80}), what is the value of (y^2)?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsReena concludes, “If the square of a real number is rational, then the number itself must be rational.” Which of the following examples disproves her conclusion?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the simplified form of (\sqrt{605}-\sqrt{320}+\sqrt{125})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student says, “The sum of two irrational numbers is always irrational.” Which of the following expressions is a counterexample to this statement?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich is the simplified form of (\frac{\sqrt{11}+\sqrt{6}}{\sqrt{11}-\sqrt{6}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf \(p\) is a non-zero rational number and \(q\) is an irrational number, which of the following expressions must always be irrational?Class 9Number SystemsIrrational numbersLevel 15Expert 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