Mathematics
Square root spiral
Practice questions
In the square root spiral, the first right triangle has perpendicular sides (1) and (1). Which point does its hypotenuse length give?If a square root spiral has radius ( \sqrt{8} ) at a step and a perpendicular unit segment (1) is added, what will be the next radius?To construct ( \sqrt{5} ) in a square root spiral, what type of segment is drawn on the radius ( \sqrt{4} )?In a square root spiral, if (OP_n=\sqrt{n}), what length is kept for (P_nP_{n+1})?A student constructed ( \sqrt{7} ) and then did not draw the next unit side perpendicular. Which conclusion is correct?In a square root spiral, after ( \sqrt{2} ), how many new unit segments are added to reach ( \sqrt{10} )?If point (P_6) in the spiral satisfies (OP_6=\sqrt{6}), what is the area of the next right triangle formed?In a square root spiral, ( \sqrt{13} ) is an example of representing which type of number on the number line?If \(OP_k=\sqrt{k}\) and \(OP_{k+1}=\sqrt{17}\), what is the value of (k)?In the square root spiral, how far is the ( \sqrt{9} ) point from the origin?Which statement correctly expresses the recursive construction of a square root spiral?If the hypotenuse at a step is (5) units and the next unit perpendicular is drawn, what is the next hypotenuse length?In the square root spiral, what is the difference between the squares of two consecutive radii forming \( \sqrt{20} \) and \( \sqrt{21} \)?If a unit perpendicular is added to the radius \( \sqrt{14} \) to form a new hypotenuse, what is the ratio of the squares of the new and old hypotenuses?Up to which point will the spiral have (11) radius-points if it starts from ( \sqrt{1} )?In the square root spiral, which hypotenuse is already formed just before constructing ( \sqrt{18} )?A student says that in a square-root spiral, each new radius is obtained by directly adding 1 to the previous radius. What is the correct evaluation of this statement?If the triangle at the ( \sqrt{12} ) step is formed by ( \sqrt{11} ) and (1), which is its hypotenuse?In constructing ( \sqrt{3} ) and ( \sqrt{4} ) in a square root spiral, what remains common?If the spiral is constructed up to \( \sqrt{27} \), in which interval will the final distance from the origin lie?