Mathematics
Square root spiral
Practice questions
Which number can be constructed on the square root spiral but may be difficult to place exactly by direct measurement on the number line?If a perpendicular of (1) unit is drawn on the hypotenuse \(\sqrt{3}\), which number will the new hypotenuse represent?In the square root spiral, if (OP_k=\sqrt{k+1}), for which (k) will (\sqrt{21}) be obtained?If the first segment (OA) is mistakenly taken as (2) units and (AB=1), what will be the first hypotenuse?In a square root spiral, when a perpendicular segment of length 1 is added at the end of the previous hypotenuse at each step, which statement about the new hypotenuse is correct?In a square root spiral, on what basis is the direction of every new (1) unit segment decided?Which option gives the correct process to construct (\sqrt{8})?If (OP=\sqrt{m}) and the next hypotenuse is (OQ=\sqrt{m+1}), what is the length of (PQ)?Which relation is correct for consecutive steps of the square root spiral?Which property correctly describes the construction of each new right triangle in a square root spiral?In a square root spiral, (\sqrt{12}) is obtained from which numbered right triangle if the first triangle gives (\sqrt{2})?If the (10)th right triangle is constructed in a square root spiral, what will its hypotenuse represent?What is the difference between the squares of the hypotenuses (\sqrt{2}) and (\sqrt{3}) in the spiral?Which option shows the correct initial sequence of lengths in a square root spiral?How many new perpendicular segments of (1) unit are drawn to construct up to (\sqrt{27}), if (OA=1) is the initial segment?If (\sqrt{16}) is constructed on the spiral, what is its actual numerical value?At which step is a hypotenuse of length (3) units obtained for the first time?If (OP=\sqrt{30}) and (OQ=\sqrt{31}) are consecutive hypotenuses, what is (PQ) equal to?Which option shows an incorrect construction in a square root spiral?If a student obtains (\sqrt{18}) by drawing a parallel segment of (1) unit on (\sqrt{17}), what is the mistake?