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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।

MathematicsA student says that \(5+\sqrt{3}\) may be a rational number. Which argument correctly identifies the error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student says, “If \(\sqrt{3}\) is irrational, then \(5\sqrt{3}\) is also irrational.” Which argument correctly proves the statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhich number-theoretic fact is used decisively while proving the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsAmit claims that \(4\sqrt{3}\) is a rational number. Which argument correctly shows the error in his claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsSuppose \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are integers. Which condition on \(m\) and \(n\) is necessary at the start of a proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRima says that \(\sqrt{2}\) is rational because its decimal form begins with 1.414.... What is the correct error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIn the proof by contradiction that \(\sqrt{2}\) is irrational, if \(\sqrt{2}=\frac{p}{q}\) is assumed where \(p,q\) are coprime, which conclusion creates a contradiction with the initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, which property is used to conclude \(3\mid p\) from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhich of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIn which option is the quotient of two irrational numbers rational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIf a rectangle has length (\sqrt{41}+\sqrt{17}) and breadth (\sqrt{41}-\sqrt{17}), what will be its area?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsLet r be a non-zero rational number and x be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich is the rationalised form of (\frac{12}{\sqrt{43}-\sqrt{31}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the simplified form of (\sqrt{726}-\sqrt{486}+\sqrt{150})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich of the following examples shows that the product of two irrational numbers can be rational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich is the simplified form of (\frac{\sqrt{31}+\sqrt{19}}{\sqrt{31}-\sqrt{19}})?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student says, “The product of two irrational numbers is always irrational.” Which of the following examples proves that the statement is wrong?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsIn the number \(0.101001000100001\ldots\), the number of zeros between two successive 1s increases by one each time. A student says that it is rational because it contains only the digits 0 and 1. Which is the correct evaluation of the student's argument?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhat is the value of ((\sqrt{125}+\sqrt{320})^2)?Class 9Number SystemsIrrational numbersLevel 15Expert