Answer
$\sqrt{100.5} \approx 10.025$
Work Step by Step
Let $y = \sqrt{x}$
$\frac{dy}{dx} = \frac{1}{2}x^{-1/2}$
$\frac{dy}{dx} = \frac{1}{2~\sqrt{x}}$
$dy = \frac{1}{2~\sqrt{x}}~dx$
Let $x = 100$ and let $dx = 0.5$
$dy = \frac{1}{2~\sqrt{100}}~(0.5)$
$dy = \frac{0.5}{20}$
$dy = \frac{1}{40}$
We can find an approximation for $\sqrt{100.5}$
$\sqrt{100.5} \approx \sqrt{100} +\frac{1}{40}$
$\sqrt{100.5} \approx 10+\frac{1}{40}$
$\sqrt{100.5} \approx 10.025$
