## Intermediate Algebra (12th Edition)

$L=CZ^2$
$\bf{\text{Solution Outline:}}$ To solve the given formula, $Z=\sqrt{\dfrac{L}{C}}$ for $L ,$ square both sides and then use the properties of equality to isolate the needed variable. $\bf{\text{Solution Details:}}$ Squaring both sides of the given formula results to \begin{array}{l}\require{cancel} (Z)^2=\left( \sqrt{\dfrac{L}{C}} \right)^2 \\\\ Z^2=\dfrac{L}{C} .\end{array} 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} Z^2(C)=1(L) \\\\ CZ^2=L \\\\ L=CZ^2 .\end{array}