## Intermediate Algebra (12th Edition)

$l=\dfrac{gp^2}{k}$
$\bf{\text{Solution Outline:}}$ 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}