Answer
$e=\pm\dfrac{\sqrt{6S}}{6}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
S=6e^2
,$ in terms of $
e
,$ use the properties of equality and the Square Root Principle to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{S}{6}=e^2
\\\\
e^2=\dfrac{S}{6}
.\end{array}
Taking the square root of both sides (Square Root Principle), the equation above is equivalent to
\begin{array}{l}\require{cancel}
e=\pm\sqrt{\dfrac{S}{6}}
.\end{array}
Rationalizing the denominator by multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
e=\pm\sqrt{\dfrac{S}{6}\cdot\dfrac{6}{6}}
\\\\
e=\pm\sqrt{\dfrac{6S}{36}}
\\\\
e=\pm\sqrt{\dfrac{1}{36}\cdot6S}
\\\\
e=\pm\sqrt{\left(\dfrac{1}{6}\right)^2\cdot6S}
\\\\
e=\pm\dfrac{1}{6}\sqrt{6S}
\\\\
e=\pm\dfrac{\sqrt{6S}}{6}
.\end{array}
