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Square Roots

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

MathematicsWhich length in a square root spiral is usually irrational?Class 9Number SystemsSquare root spiralLevel 23Easy MathematicsIn a square root spiral, if both perpendicular sides of the first right triangle are (1) unit, what will be the hypotenuse?Class 9Number SystemsSquare root spiralLevel 23Easy MathematicsIn constructing a square root spiral, a student uses a hypotenuse of \(\sqrt{6}\) and draws a perpendicular side of 1 unit. Which number will the new hypotenuse represent?Class 9Number SystemsSquare root spiralLevel 22Easy 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 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 MathematicsIf \(x=\sqrt{2}+\sqrt{3}\), which argument correctly disproves the assumption that \(x\) is rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf a student assumes that \(\sqrt{2}+\sqrt{3}\) is a rational number \(r\), which conclusion correctly proves a contradiction in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsA student claims that \(\sqrt{2}+\sqrt{3}\) is a rational number. Which argument correctly identifies the error in the claim?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 of the following integers has a rational square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that \(\sqrt{2}+\sqrt{3}\) is a rational number. Which argument correctly identifies the error in this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsA student claims that \(\sqrt{2}+\sqrt{3}\) is rational. Which argument correctly proves that the claim is wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsFor a positive integer \(n\), which condition identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 65Expert MathematicsFor a square with an area of 2 cm², Aarav says, “Since the area is a rational number, the perimeter of the square must also be rational.” Which is the correct evaluation of Aarav’s statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsRina is proving that \(\sqrt{12}\) is irrational. Which of the following arguments contains no error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIn the proof by contradiction for the irrationality of \(\sqrt{2}\) and \(\sqrt{3}\), which prime-number property for an integer \(n\) is used decisively?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose it is claimed that \(s=\sqrt{2}+\sqrt{3}\) is rational. Since \((\sqrt{2}+\sqrt{3})(\sqrt{3}-\sqrt{2})=1\), \(\sqrt{3}-\sqrt{2}=1/s\) would also be rational. Which equation below immediately produces a contradiction from this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsRima says, “If \(\sqrt{12}\) were rational, then \(\sqrt{3}=\frac{\sqrt{12}}{2}\) would also be rational, which contradicts the irrationality of \(\sqrt{3}\).” What is Rima’s conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that \(\sqrt{2}+\sqrt{3}\) is irrational because the sum of two irrational numbers is always irrational. What is the correct evaluation of this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student claims that \(\sqrt{12}\) is rational because 12 is not a perfect square. Which is the correct simplified form of \(\sqrt{12}\) that identifies the error in the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard