#### Answer

$K=\dfrac{mV^2}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given formula, $
V=\sqrt{\dfrac{2K}{m}}
$ for $
K
,$ 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}
(V)^2=\left( \sqrt{\dfrac{2K}{m}} \right)^2
\\\\
V^2=\dfrac{2K}{m}
.\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}
V^2(m)=1(2K)
\\\\
mV^2=2K
\\\\
\dfrac{mV^2}{2}=K
\\\\
K=\dfrac{mV^2}{2}
.\end{array}