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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 assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), which conclusion proves this assumption contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsThe diagonal of a square with side 1 unit is \(\sqrt{2}\) units long. A student wants to write it as a ratio of two integers. Which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed, where \(p\) and \(q\) are coprime, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says, “\(\sqrt{3}=\frac{6}{\sqrt{12}}\), so \(\sqrt{3}\) is rational.” What is the error in the argument?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 MathematicsA student assumes dfrac{p}{q} is in lowest terms and obtains p^2=3q^2 , where p and q are coprime. Which conclusion proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich statement correctly describes the method used to prove that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{3}=\frac{m}{n}\) is assumed, where \(m\) and \(n\) are coprime integers, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIn the proof that \(\sqrt{3}\) is irrational, if \(p^2\) is divisible by 3, which conclusion about \(p\) is correct?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 says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then when \(p\) is divisible by 3, \(q\) will also be divisible by 3. What conclusion does this statement lead to?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student assumes that ",Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsSuppose a is an integer and 3 divides \(a^2\). Which of the following conclusions is valid in the proof that \(\sqrt{3}\) is irrational?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 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 MathematicsWhich statement about √3 is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA calculator displays \(\sqrt{3}\) as 1.732. Mohan concludes that \(\sqrt{3}\) is rational. What is Mohan’s error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRiya says that \(\sqrt{2}\) is irrational because its decimal expansion never terminates. What is the flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy