Mathematics
Square root spiral
Practice questions
In a square root spiral, if (OA=1), (AB=1), and (AB \perp OA), what is the length of (OB)?If (OB=\sqrt{2}) and (BC=1) is drawn perpendicular to (OB), what is the length of (OC)?In a square root spiral, to obtain (OD=\sqrt{4}), on which previous segment is a perpendicular of (1) unit drawn?If at a certain step the previous radius is (\sqrt{8}), what will be the length of the next radius?How is the segment representing (\sqrt{7}) obtained in a square root spiral?In the spiral, if (OP_n=\sqrt{n+1}), what is the length of (OP_{12})?If the first hypotenuse in the spiral is (OB=\sqrt{2}), how many new perpendicular steps of (1) unit are needed after (OB) to reach (\sqrt{10})?In the construction of a square root spiral, what is the length of one side kept fixed in every new triangle?If the hypotenuse of a new triangle is (\sqrt{11}) and one perpendicular side is (1), what was the previous radius?Which statement is correct for the square root spiral?If \(OP=\sqrt{15}\), \(PQ=1\), and (PQ \perp OP), what is the value of \(OQ^2\)?In a square root spiral, the point representing (\sqrt{5}) comes immediately after which one?Why are segments like (\sqrt{2},\sqrt{3},\sqrt{4}) formed in a square root spiral?If the construction starts with (OA=1), how many right triangles are formed by the time (\sqrt{6}) is obtained?If the hypotenuse of the fourth constructed right triangle is asked, what is the correct length?To construct (\sqrt{13}) in a square root spiral, on which previous hypotenuse should a perpendicular of (1) unit be drawn?If the distance of a point from the origin is (\sqrt{17}), what will be the distance of the next point from the origin?Which pair correctly shows two consecutive hypotenuses of the square root spiral?If (OP=\sqrt{20}), what was the length of the hypotenuse formed just before it?Looking at (\sqrt{4}) and (\sqrt{9}) in a square root spiral, which conclusion is correct?