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Rational Numbers

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

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 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 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 of the following examples shows that the product of two irrational numbers can be rational?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 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 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 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 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 MathematicsIf \(x\) is an irrational number and \(r\) is a non-zero rational number, what type of number must \(rx\) be?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsLet \(p\) 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 MathematicsIf \(x\) is an irrational number, which of the following expressions will always be rational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich of the following decimal expansions definitely identifies the number as irrational?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 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 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 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