The first three Taylor polynomials for $f(x)=\sqrt[\phantom{2}]{25+x}$ centered at $0$ are $p_0(x)=5,p_1(x)=5+\frac{x}{10},$ and $p_2(x)=5+\frac{x}{10}-\frac{x^2}{1000}.$ Find three approximations to $\sqrt[\phantom{2}]{25\mathrm{.}2}.$

The approximation based on $p_0(x)$ is

$($Type an integer or decimal rounded to six decimal places as needed.$)$

The approximation based on $p_1(x)$ is

$($Type an integer or decimal rounded to six decimal places as needed.$)$

The approximation based on $p_2(x)$ is

$($Type an integer or decimal rounded to six decimal places as needed.$)$