Mathematics
Square root spiral
Practice questions
In a square root spiral, if the previous hypotenuse is (\sqrt{80}) and the new perpendicular is (1) unit, at what exact value will the new hypotenuse lie?While constructing a square root spiral, a student drew a perpendicular of length 1 on the segment representing \(\sqrt{17}\) and labelled the new hypotenuse as \(\sqrt{19}\). What is the error in the student's reasoning?If a student writes (\sqrt{12}+1=\sqrt{13}) while finding the next hypotenuse from (\sqrt{12}), what is the correct correction?In a square root spiral, drawing a (1) unit perpendicular on (\sqrt{143}) forms which hypotenuse and where will its value lie?To construct (\sqrt{35}) in a square root spiral, which previous hypotenuse and new perpendicular side are correct?In a square root spiral, how is the line segment representing \(\sqrt{n}\) obtained, where \(n\) is a positive integer?What is the main reason that the successive hypotenuses in a standard square root spiral have lengths \(1, \sqrt{2}, \sqrt{3}, \sqrt{4}\), and so on?If the new hypotenuse in a square root spiral is (\sqrt{226}), what was the immediately previous hypotenuse and in which interval does the new value lie?While forming √4 from √3 in a square root spiral, which statement contains a logical error?In a square root spiral, why does the next hypotenuse after \(\sqrt{168}\) simplify specially?Which statement is correct when comparing \(\sqrt{242}\) and \(\sqrt{256}\) in a square root spiral?In a standard square root spiral, which group of hypotenuse labels represents points at integral distances from the origin?Which inequality is correct to identify the position of \(\sqrt{125}\) in a square root spiral?Which statement is correct about the point representing \(\sqrt{49}\) in a square root spiral?What is the correct reason for constructing (\sqrt{8}) from (\sqrt{7}) and (1) in a square root spiral?Which statement is correct when comparing the hypotenuse formed after (\sqrt{63}) and (\sqrt{65}) in a square root spiral?At a step in a square root spiral, the hypotenuse is (\sqrt{m}). If (m) is exactly (1) less than a perfect square, what will the next hypotenuse be like?What is the correct position of (\sqrt{288}) in a square root spiral?Why is using (\sqrt{46}) and a (2) unit perpendicular wrong for constructing (\sqrt{48}) by the usual rule of square root spiral?While constructing a square root spiral, a student says that \(\sqrt{26}\) should be shown at the point 5 because 26 is very close to 25. What is the correct correction of this error?