In a square root spiral, why is using \(\sqrt{4}\) and \(1\) correct for constructing \(\sqrt{5}\)?

Correct answer: Because \((\sqrt{5})^2=(\sqrt{4})^2+(1)^2=4+1=5\).

In a square root spiral, the new hypotenuse comes from Pythagoras’ theorem on a right triangle: the hypotenuse squared equals the sum of the squares of perpendicular sides. Here the perpendicular sides are \(\sqrt{4}\) and \(1\). So:
\[
(\sqrt{5})^2=(\sqrt{4})^2+(1)^2=4+1=5,
\]
which means the hypotenuse is \(\sqrt{5}\). Thus option A is correct.