Suppose you want to approximate $\sqrt[\phantom{2}]{12}$ using four terms of a Taylor series. Compare the accuracy of the approximations obtained using Taylor series for $\sqrt[\phantom{2}]{x}$ centered at $9$ and $16.$

The accuracy of the approximations obtained using Taylor series for $\sqrt[\phantom{2}]{x}$ centered at $9$ and $16$ are about $$ and $$ respectively. It is better to use the approximation obtained using the Taylor series for $\sqrt[\phantom{2}]{x}$ centered at $($Round to six decimal places as needed.$)$