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Square Root 2

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 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 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 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 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 MathematicsWhich conclusion is correct in the proof that √2 is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Medium 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 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 MathematicsFrom (b^2=2k^2) what conclusion is obtained about (b)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf (a=2k) and (a^2=2b^2) then which relation follows?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 MathematicsWhat is known about (a^2) from (a^2=2b^2)?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 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 MathematicsA student assumes that ",Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhat does assuming (\sqrt{2}) as (\frac{p}{q}) mean?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 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 MathematicsSuppose \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are integers. Which condition on \(m\) and \(n\) is necessary at the start of a proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRima says that \(\sqrt{2}\) is rational because its decimal form begins with 1.414.... What is the correct error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy