Answer
$1$
Work Step by Step
Note that, if $f(x)\ge0$, then
$\lim _{x\rightarrow c}\sqrt {f\left( x\right) }=\sqrt {\lim _{x\rightarrow c}f\left( x\right) }$
Thus,
$\lim _{x\rightarrow 0}\sqrt {1-2x}=\sqrt {\lim _{x\rightarrow 0}\left( 1-2x\right) }$
Since $\lim _{x\rightarrow c}f(x) = f(c)$, then
$\sqrt {\lim _{x\rightarrow 0}\left( 1-2x\right) }
\\=\sqrt {1-2\times 0}
=\sqrt {1}
\\=1$
