Answer
$k=\dfrac{1}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{6k-1}=1
,$ 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{6k-1} \right)^2=(1)^2
\\\\
6k-1=1
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
6k=1+1
\\\\
6k=2
\\\\
k=\dfrac{2}{6}
\\\\
k=\dfrac{1}{3}
.\end{array}
Upon checking, $
k=\dfrac{1}{3}
$ satisfies the original equation.