Answer
$\Delta x = dx = 0.8$
$\Delta y = 0.34164$
$dy = 0.4$
We can see a sketch below.
Work Step by Step
$y = \sqrt{x-2}$
$\Delta x = dx = 0.8$
When $x = 3$, then $y = \sqrt{3-2}= 1$
When $x = 3.8$, then $y = \sqrt{3.8-2} = 1.34164$
$\Delta y = 1.34164-1 = 0.34164$
We can find the value of $dy$:
$\frac{dy}{dx} = \frac{1}{2}(x-2)^{-1/2} = \frac{1}{2~\sqrt{x-2}}$
$dy = \frac{1}{2~\sqrt{x-2}}~dx$
$dy = \frac{1}{2~\sqrt{3-2}}~(0.8)$
$dy = 0.4$
We can see a sketch below.
