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

MathematicsWhile proving (\sqrt{3}) irrational, what is the first rational assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsIn proving irrationality of (\sqrt{2}), with which assumption does contradiction method begin?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy 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 MathematicsIn the proof of \(\sqrt{2}\), what is the first conclusion after getting \(a^2=2b^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhat is the main aim of proving irrationality of (\sqrt{2}) and (\sqrt{3})?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 MathematicsIn the proof of √2, when both a and b are even, which conclusion should not be taken?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Medium 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 MathematicsIn both proofs in what form is the number first written?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 MathematicsWhy is it necessary to take (\frac{p}{q}) in lowest form in the proof of (\sqrt{3})?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 MathematicsIf a number is not divisible by (3), then its square is surely not divisible by what?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf the square of a number is not even then what type is the number?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