Mathematics
Square root spiral
Practice questions
In a square root spiral, if the new hypotenuse is √(n+1) and it is the whole number 12, what was the previous hypotenuse?Which of the following sequences is most correct for constructing \(\sqrt{10}\) in a square root spiral?While identifying the interval of (\sqrt{195}) in a square root spiral, which mistake is most likely?Why does adding a (1) unit perpendicular to hypotenuse (\sqrt{n}) in a square root spiral give new hypotenuse (\sqrt{n+1})?In a square root spiral, which of the following labelled hypotenuses represents a rational length?In a square root spiral, the length of the segment drawn from the origin to an outer vertex is
\(\sqrt{n}\). For which type of \(n\) will this length be a rational number?In constructing a square root spiral, each new triangle is formed by adding a side of length 1 unit perpendicular to the hypotenuse of the previous triangle. What is the hypotenuse of the new triangle?To construct (\sqrt{224}) in a square root spiral, what is the correct previous hypotenuse and in which interval will the formed hypotenuse lie?After obtaining \(\sqrt{18}\) using the square root spiral, Riya marks it at 4.5 on the number line. Which comment about her marking is correct?Which step is most precise while marking (\sqrt{2}) on the number line using a square root spiral?A student says that a base of length 10 units must first be drawn to represent \(\sqrt{10}\) on the square root spiral. Which option correctly explains the student's error?Why are (\sqrt{4}) and (1) correct sides for constructing (\sqrt{5}) in a square root spiral?Before placing \(\sqrt{440}\) on the number line using a square root spiral, which interval is correct?If the (k)-th hypotenuse in a square root spiral is considered as (\sqrt{k}), which hypotenuse is (\sqrt{25}), and what is its value?A student says that in a square root spiral, the length of the next hypotenuse after \(\sqrt{14}\) will be \(\sqrt{14}+1\). Which reasoning correctly shows the error in this statement?Which statement is most precise from the construction point of view in a square root spiral?Which construction rule is followed to form each new right triangle in a square root spiral?What is the correct interval for (\sqrt{624}) in a square root spiral?In a square root spiral, if the hypotenuse (\sqrt{n+1}) formed after (\sqrt{n}) is irrational, what can be definitely true?Why is a (1) unit perpendicular on (\sqrt{20}) sufficient to construct (\sqrt{21}) in a square root spiral?