Answer
$a=19$
Work Step by Step
The given equation is
$\Rightarrow \sqrt {a-3}+5=9$
Subtract $5$ from each side.
$\Rightarrow \sqrt {a-3}+5-5=9-5$
Simplify.
$\Rightarrow \sqrt {a-3}=4$
Square each side of the equation.
$\Rightarrow (\sqrt{a-3})^2=4^2$
Simplify.
$\Rightarrow a-3=16$
Add $3$ to each side.
$\Rightarrow a-3+3=16+3$
Simplify.
$\Rightarrow a=19$
Check $a=19$.
$\Rightarrow \sqrt {a-3}+5=9$
$\Rightarrow \sqrt {19-3}+5=9$
$\Rightarrow \sqrt {16}+5=9$
$\Rightarrow \sqrt {4^2}+5=9$
$\Rightarrow 4+5=9$
$\Rightarrow 9=9$
True.
Hence, the solution is $a=19$.
