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Rational Numbers

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

MathematicsA student claims that \(5+\sqrt{3}\) may be rational because 5 is rational. Which is the correct refutation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student says, “For a non-zero rational number \(a\), \(a\sqrt{3}\) can be rational.” Which argument correctly explains the error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsA student claims that \(1+\sqrt{2}\) is rational because 1 is a rational number. Which argument correctly refutes the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsIt is known that \(\sqrt{3}\) is irrational. Which of the following conclusions must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that the decimal expansion of \(\sqrt{2}\) never terminates, so it is irrational. Which of the following arguments rigorously proves this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsRavi claims that \(7+\sqrt{2}\) is a rational number because 7 is rational. What is the error in Ravi’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student claims that \(3\sqrt{2}\) is rational because 3 is a rational number. What is the correct evaluation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich of the following numbers must be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich of the following conclusions about radicals is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student claims that \(5+\sqrt{3}\) is rational because 5 is rational. Which is the correct refutation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student believes that any number with an infinite decimal expansion must be irrational. Which example disproves this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsRiya says that \(\sqrt{3}\) is rational because its decimal form is \(1.732\). Which statement correctly identifies the error in her claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhy are p and q chosen coprime in √3 = p/q?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that since 5 is a rational number, \(5+\sqrt{3}\) must also be rational. Which statement correctly identifies the error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich initial assumption is made to prove the irrationality of \(\sqrt{3}\) by the method of contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\) in lowest terms. If \(p\) is shown to be divisible by 3, which conclusion about \(q\) is needed to obtain a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich of the following numbers cannot be written as a ratio \(p/q\) of two integers, where \(q\ne0\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option is a wrong start in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student says, “3 is not a perfect square, so \(\sqrt{3}\) is irrational.” Which step is needed to complete this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student has to prove that \(1+\sqrt{3}\) is irrational. Which of the following arguments is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium