use differential to approximate Square root 17.
$\displaystyle \sqrt{17}=f(x+\Delta x)$
Where $\displaystyle x=16$, $\displaystyle \Delta x=1$, and $\displaystyle f(x)=\sqrt{x}$
$\displaystyle f(x+\Delta x)\approx f(x)+{f}'(x)\Delta x$
$\displaystyle {f}'(x)=\frac{\mathrm{d}[\sqrt{x}]}{\mathrm{d} x}=\frac{1}{2\sqrt{x}}$
$\displaystyle f(17)\approx f(16)+(1){f}'(16)=4+\frac{1}{8}=33/8=4.125$
I hope this helps.