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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।

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 MathematicsRiya says that since a calculator displays \(\sqrt{2}\) as 1.414, \(\sqrt{2}\) is a rational number. What is the error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. The student obtains \(p^2=3q^2\). Which conclusion from this step establishes the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says, “1.732 is a terminating decimal and is very close to \(\sqrt{3}\), so \(\sqrt{3}\) is rational.” What is the main error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says that \(\sqrt{3}\) is rational because \(1.7^2=2.89\), which is very close to 3. What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student claims that √12 is irrational because √12 = 2√3. Which statement is needed to make this argument valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsAman assumes that ext{\(\sqrt{3}=\frac{p}{q}\)}, where ext{\(p\)} and ext{\(q\)} are coprime. On squaring, he gets ext{\(p^2=3q^2\)}. Aman says, “ ext{\(3\mid p^2\)} does not necessarily imply ext{\(3\mid p\)}.” What is the correct evaluation of Aman’s statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says, “If n is an integer, then \(\sqrt{n}\) will also be an integer.” Which example is most suitable to disprove this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf \(\sqrt{2}\) is assumed to be \(\frac{p}{q}\) in lowest terms, which conclusion creates the contradiction in proving that it is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(\sqrt{3}=\frac{p}{q}\) where \(p\) and \(q\) are coprime, which statement follows from \(p^2=3q^2\) and creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsReema says, “The decimal expansion of \(\sqrt{3}\) is infinite, so it is irrational.” What is the flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhile proving the irrationality of \(\sqrt{2}\), a student assumes \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. On obtaining \(p^2=2q^2\), the student immediately says that \(q\) is even. How should the teacher correct the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 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 MathematicsA student writes that \(\sqrt{3}=1.732\), so \(\sqrt{3}\) is rational. What is the correct correction to this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhich statement creates a contradiction in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. Which conclusion produces a contradiction to this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIf \(\sqrt{3}\) is assumed to be rational and written as \(\frac{p}{q}\), which condition is necessary for \(p\) and \(q\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsAfter squaring \(\sqrt{3}=\frac{r}{s}\), which equation is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says, “\(\sqrt{3}=1.732\), so \(\sqrt{3}\) is rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsRiya says, “Since 2 is an integer, \(\sqrt{2}\) must also be a rational number.” What is Riya’s error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy