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Proof Of Irrationality

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

MathematicsWhich condition guarantees that the square root of a natural number \(n\) is rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student claims that \(\sqrt{3}\) is rational because its decimal form is 1.732 and \(1.732=\frac{1732}{1000}\). What is the error in the student’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsRima says, “\(\sqrt{3}=1.732\); therefore, \(\sqrt{3}\) is rational.” What is the main error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich of the following numbers can be proved irrational using its prime factorisation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhich option identifies an invalid shortcut in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn a proof of irrationality, if 3 is prime and 3 divides the square p² of an integer p, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsWhich statement correctly identifies why \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich option shows an invalid shortcut in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf b^2=3a^2 is obtained when b is in lowest form, which property is used to prove that b is divisible by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsFor a positive integer \(n\), which of the following statements is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says, “If the area of a square is rational, then its side must also be rational.” Which of the following examples disproves the statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf assuming √3 is rational breaks the coprime condition, which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student claims that \(\sqrt{3}\) is rational because its square, \(3\), is a rational number. Which statement about this argument is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option shows the correct logical chain in the proof of (√3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option shows the correct logical chain in the proof of (√2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich of the following numbers has an irrational positive square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student claims that \(\sqrt{3}\) is rational because \(1.7^2=2.89\), which is very close to 3. What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium 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 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 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