Mathematics
Square root spiral
Practice questions
In a square root spiral, in which situation will the hypotenuse not be a whole number?While constructing a square root spiral, a student drew a perpendicular of length 1 unit on the hypotenuse \(\sqrt{7}\). The student claims that the new hypotenuse will be \(\sqrt{6}\), not \(\sqrt{8}\). What is the correct evaluation of the student's claim?Just before constructing (\sqrt{121}) in a square root spiral, which hypotenuse should be present?Why do both (\sqrt{2}) and (\sqrt{3}) lie between (1) and (2) on the number line in a square root spiral?While observing a square root spiral, Riya says, “The length of each new hypotenuse is exactly 1 unit more than the previous hypotenuse.” What is the correct evaluation of Riya’s statement?Which relation is correct in forming (\sqrt{2}) from (\sqrt{1}) in a square root spiral?What must be done on the previous hypotenuse to construct (\sqrt{75}) in a square root spiral?In a square root spiral, what is the distance of the point representing \(\sqrt{n}\) from the origin?When (\sqrt{65}) is formed from (\sqrt{64}) in a square root spiral, which statement is correct?To show (\sqrt{n}) on the number line using a square root spiral, which length is taken in the compass?In a square root spiral, which hypotenuse comes after \(\sqrt{45}\) and in which interval does it lie?Which tool is correctly matched with its work in a square root spiral?Which construction method is correct for forming each new right triangle in a square root spiral?What is common in the construction of \(\sqrt{2}\) and \(\sqrt{3}\) in a square root spiral?If (\sqrt{15}) has been constructed in a square root spiral, in the next step the hypotenuse length will be equal to which whole number?What is the correct process to construct √7 in a square root spiral?Which statement is wrong for a square root spiral and why?What is the correct way to place length (\sqrt{2}) on the number line using a square root spiral?If a student writes √n + 1 = √(n+1) to state the next hypotenuse in a square root spiral, what is the correction?What is the main idea of showing irrational numbers on the number line using a square root spiral?