Answer
$M=\dfrac{Fr^2}{m}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given formula, $
r=\sqrt{\dfrac{Mm}{F}}
$ for $
M
,$ square both sides and then use cross-multiplication to isolate the needed variable.
$\bf{\text{Solution Details:}}$
Squaring both sides of the given formula results to
\begin{array}{l}\require{cancel}
(r)^2=\left( \sqrt{\dfrac{Mm}{F}} \right)^2
\\\\
r^2=\dfrac{Mm}{F}
.\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}
r^2(F)=1(Mm)
\\\\
Fr^2=Mm
\\\\
\dfrac{Fr^2}{m}=M
\\\\
M=\dfrac{Fr^2}{m}
.\end{array}
