Answer
$d=\pm\dfrac{\sqrt{skw}}{kw}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
s=kwd^2
,$ in terms of $
d
,$ 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}{kw}=d^2
\\\\
d^2=\dfrac{s}{kw}
.\end{array}
Taking the square root of both sides (Square Root Principle), the equation above is equivalent to
\begin{array}{l}\require{cancel}
d=\pm\sqrt{\dfrac{s}{kw}}
.\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}
d=\pm\sqrt{\dfrac{s}{kw}\cdot\dfrac{kw}{kw}}
\\\\
d=\pm\sqrt{\dfrac{skw}{(kw)^2}}
\\\\
d=\pm\sqrt{\dfrac{1}{(kw)^2}\cdot skw}
\\\\
d=\pm\sqrt{\left( \dfrac{1}{kw}\right)^2\cdot skw}
\\\\
d=\pm\dfrac{1}{kw}\sqrt{skw}
\\\\
d=\pm\dfrac{\sqrt{skw}}{kw}
.\end{array}
