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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।

MathematicsAfter constructing \(\sqrt{55}\) in a square root spiral, what will be the next hypotenuse and in which interval will it lie?Class 9Number SystemsSquare root spiralMedium MathematicsWhat type of number is \(\sqrt{20}\) in a square root spiral and why?Class 9Number SystemsSquare root spiralMedium MathematicsIn a square root spiral, what type of number does \(\sqrt{10}\) represent?Class 9Number SystemsSquare root spiralEasy MathematicsWhich length in a square root spiral is usually irrational?Class 9Number SystemsSquare root spiralEasy 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 spiralEasy 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 spiralEasy 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 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Expert MathematicsWhich of the following integers has a rational square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Expert 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 3Hard