Answer
$l=\dfrac{gp^2}{k}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
p=\sqrt{\dfrac{kl}{g}}
,$ in terms of $
l
,$ square both sides. Then use the laws of exponents and the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Squaring both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
(p)^2=\left( \sqrt{\dfrac{kl}{g}} \right)^2
\\\\
p^2=\dfrac{kl}{g}
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
g(p^2)=\left( \dfrac{kl}{g} \right) g
\\\\
gp^2=kl
\\\\
\dfrac{gp^2}{k}=l
\\\\
l=\dfrac{gp^2}{k}
.\end{array}
