Mathematics
Square root spiral
Practice questions
While locating \(\sqrt{10}\) on the number line using a square root spiral, a student says it will be to the right of 4 because 10 is greater than 4. What is the correct correction to this error?While constructing a square root spiral, a student says that to obtain \(\sqrt{8}\) after \(\sqrt{7}\), a perpendicular of length 1 should be drawn to the previous hypotenuse \(\sqrt{7}\). What is the status of the student's statement?Why are both a (1) unit perpendicular and a right angle necessary in a square root spiral?While constructing a square root spiral, a student uses 2 cm instead of 1 cm as the perpendicular side of every new right triangle. Which conclusion about the figure is correct?While constructing a square root spiral, between which two segments is each new right angle formed?Which sequence is represented by the lengths of successive hypotenuses in a standard square root spiral?In a square root spiral, what type of number is represented by the point for \(\sqrt{17}\)?Just before constructing (\sqrt{255}) in a square root spiral, which hypotenuse will be present?At medium level, which is the most precise summary of a square root spiral?If a (1) unit perpendicular is drawn on hypotenuse (\sqrt{120}) in a square root spiral, what will be the new hypotenuse and in which interval will it lie?In a square root spiral, if the previous hypotenuse is (\sqrt{18}), by which calculation will the new hypotenuse be obtained?A student says, “The new hypotenuses in a square root spiral represent square roots of perfect squares only.” How should this statement be judged?If the new hypotenuse (\sqrt{35}) is formed in a square root spiral, which hypotenuse should come just before it?In a square root spiral, in which interval will the length \(\sqrt{45}\) lie on the number line?A student constructs \(\sqrt{13}\) on a square root spiral by drawing a perpendicular segment of length 1 at the point for \(\sqrt{12}\) and joining its end to the origin. Why is this reasoning correct? What is the square of the new hypotenuse?What is the main reason that the successive hypotenuses in a square root spiral have lengths \(\sqrt{2}, \sqrt{3}, \sqrt{4}\), and so on?Which statement about \(\sqrt{72}\) and \(\sqrt{81}\) in a square root spiral is correct?To construct (\sqrt{120}) in a square root spiral, on which previous hypotenuse will a (1) unit perpendicular be drawn?In a square root spiral, in which interval will \(\sqrt{120}\) lie on the number line?Why will the usual sequence break if a (4) unit perpendicular is used instead of (1) unit in a square root spiral?