Answer
$3$
Work Step by Step
Note that, if $f(x) \ge 0$,
$\lim _{x\rightarrow c}\sqrt {f\left( x\right) }=\sqrt {\lim _{x\rightarrow c}f\left( x\right) }$
Thus,
$\lim _{x\rightarrow 1}\sqrt {5x+4}
\\=\sqrt {\lim _{x\rightarrow 1}\left( 5x+4\right) }$
Since $\lim _{x\rightarrow c}f(x) = f(c)$, then
$\\=\sqrt {\lim _{x\rightarrow 1}\left( 5x+4\right) }
\\=\sqrt {5\times 1+4}
\\=\sqrt {9}
\\=3$
