#### Answer

$x=48$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{x+1}=7
,$ square both sides of the equation and then isolate the variable. Then, do checking of the solution with the original equation.
$\bf{\text{Solution Details:}}$
Squaring both sides of the equation results to
\begin{array}{l}\require{cancel}
\left( \sqrt{x+1} \right)^2=(7)^2
\\\\
x+1=49
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x=49-1
\\\\
x=48
.\end{array}
Upon checking, $
x=48
$ satisfies the original equation.