Answer
$d=\pm\dfrac{\sqrt{kR}}{R}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
R=\dfrac{k}{d^2}
,$ in terms of $
d
,$ use the properties of equality and the Square Root Principle to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $\dfrac{a}{b}=\dfrac{c}{d}$ implies $ad=bc$ or sometimes referred to as cross-multiplication, the equation above is equivalent to
\begin{array}{l}\require{cancel}
R(d^2)=1(k)
\\\\
Rd^2=k
\\\\
d^2=\dfrac{k}{R}
.\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{k}{R}}
.\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{k}{R}\cdot\dfrac{R}{R}}
\\\\
d=\pm\sqrt{\dfrac{kR}{R^2}}
\\\\
d=\pm\sqrt{\dfrac{1}{R^2}\cdot kR}
\\\\
d=\pm\sqrt{\left( \dfrac{1}{R} \right)^2\cdot kR}
\\\\
d=\pm\dfrac{1}{R}\sqrt{kR}
\\\\
d=\pm\dfrac{\sqrt{kR}}{R}
.\end{array}
