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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।

MathematicsWhy is \(\frac{p}{q}\) taken in lowest terms while proving the irrationality of \(\sqrt{2}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf sqrt{2} is an irrational number, which of the following numbers must also be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says, “3 is a rational number, so \(\sqrt{3}\) must also be rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsRima says that \(5+\sqrt{2}\) is a rational number because 5 is rational. Which is the correct evaluation of her statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student says that \(4+\sqrt{3}\) is a rational number because 4 is rational. Which statement correctly explains the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of \(\sqrt{3}\), which conclusion is rejected by the rational assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhat is the highest common factor of two coprime numbers?Class 9Number SystemsRational numbersLevel 21Easy MathematicsA student claims that \(\sqrt{3}=\frac{6}{10}\) because a decimal number close to 3 can be written. What is the error in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhen a rational number is written in lowest form as p/q, what is true about p and q?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf a number can be written in the form \(\frac{p}{q}\), where \(p\) and \(q\) are coprime integers and \(q\neq 0\), what is it called?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsRima says that if the decimal expansion of a number is infinite but non-repeating, then the number is rational. What is the error in Rima's statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student claims that \(\sqrt{2}\) is rational because \(1.414\) can be written as \(\frac{1414}{1000}\). What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsAssuming that \(\sqrt{3}\) is irrational, which of the following numbers must be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhich of the following correctly describes the nature of the number \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student claims that \(\sqrt{2}\) is rational because \(1.414=\frac{1414}{1000}\). What is the main error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRima claims that \(2+\sqrt{3}\) is a rational number. Which is the most appropriate argument to prove her claim wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIf p/q is in lowest form, what is true about p and q?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student assumes that \(\sqrt{3}\) can be written as \(\frac{a}{b}\) in lowest terms. During the proof, it is found that 3 divides both \(a\) and \(b\). Which conclusion about the student’s assumption is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy 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