#### Answer

$d=\pm\dfrac{\sqrt{ksI}}{I}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
I=\dfrac{ks}{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}
I(d^2)=1(ks)
\\\\
Id^2=ks
\\\\
d^2=\dfrac{ks}{I}
.\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{ks}{I}}
.\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{ks}{I}\cdot\dfrac{I}{I}}
\\\\
d=\pm\sqrt{\dfrac{ksI}{I^2}}
\\\\
d=\pm\sqrt{\dfrac{1}{I^2}\cdot ksI}
\\\\
d=\pm\sqrt{\left( \dfrac{1}{I}\right)^2\cdot ksI}
\\\\
d=\pm\dfrac{1}{I}\sqrt{ksI}
\\\\
d=\pm\dfrac{\sqrt{ksI}}{I}
.\end{array}