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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।

MathematicsWhile proving that \(\sqrt{2}\) is irrational by contradiction, assume \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. After obtaining \(p^2=2q^2\) and showing that \(p\) is even, which conclusion must be established to get a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy 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 MathematicsA student writes: “3 is not a perfect square, so \(\sqrt{3}\) is irrational.” What is the most appropriate evaluation of this statement in a question asking to prove the irrationality of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich of the following numbers has an irrational square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that \(\sqrt{3}\) is rational because its value is approximately 1.73. Which comment about this statement is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne0\), then \(p^2=3q^2\) proves only that \(p\) is divisible by 3. What is the correct next conclusion in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich of the following statements correctly describes the main idea used in proving that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring both sides, \(3q^2=p^2\) is obtained. Which conclusion proves the assumption wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that \(\sqrt{3}\) is rational because 1.732 is a terminating decimal. What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich of the following statements is the correct basis for proving that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then from \(p^2=2q^2\) only \(p\) is even and nothing can be said about \(q\). What is the student's error?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 MathematicsIn the contradiction proof for the irrationality of \(\sqrt{3}\), assume that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. Why is the condition that \(p\) and \(q\) are coprime necessary?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich option gives the correct short order of the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Medium MathematicsWhich statement is the key conclusion in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then even if \(p\) is divisible by 3, \(q\) need not be divisible by 3. Why is the statement incorrect?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhen irrationality of \(\sqrt{3}\) is proved, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student claims that \(\sqrt{3}=\frac{26}{15}\). Which of the following checks immediately proves that this claim is false?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says, “\(3\) is an integer, so \(\sqrt{3}\) is rational.” What is the main error in this reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{2}\) is assumed to be \(\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, which conclusion creates the contradiction in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy