# How do you solve for m in K=1/2 m^2?

Aug 29, 2016

$m = {\left(2 \cdot K\right)}^{0.5}$

#### Explanation:

Let me compute m step by step.

${m}^{2} = 2 \cdot K$

Now square root both sides:

$m = {\left(2 \cdot K\right)}^{0.5}$

Aug 29, 2016

$m = \pm \sqrt{K}$

#### Explanation:

Isolate m, step by step. This is also called making $m$ the subject of the formula.

It feels more comfortable to have $m$ on the left hand side. We may just turn the equation around to achieve this.

$K = \frac{1}{2} {m}^{2}$

$\frac{1}{2} {m}^{2} = K \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \times 2$

$\cancel{2} \times \frac{1}{\cancel{2}} {m}^{2} = K \times 2$

m^2 = Kcolor(white)(............................................) "find" sqrt

$m = \pm \sqrt{K}$