Solve frac{sqrt{(k-m)}}{n}=1/m

$$\frac{ \sqrt{ (k-m) } }{ n } = \frac{ 1 }{ m }$$

Solve for k

$$k=m+\left(\frac{n}{m}\right)^{2}$$

$$\left(m>0\text{ and }n>0\right)\text{ or }\left(m<0\text{ and }n<0\right)$$

Steps for Solving Radical Equations

Divide both sides by n^{-1}.

$$\frac{\frac{1}{n}\sqrt{k-m}n}{1}=\frac{1}{m\times \frac{1}{n}}$$

Dividing by n^{-1} undoes the multiplication by n^{-1}.

$$\sqrt{k-m}=\frac{1}{m\times \frac{1}{n}}$$

Divide \frac{1}{m} by n^{-1}.

$$\sqrt{k-m}=\frac{n}{m}$$

Square both sides of the equation.

$$k-m=\frac{n^{2}}{m^{2}}$$

Subtract -m from both sides of the equation.

$$k-m-\left(-m\right)=\frac{n^{2}}{m^{2}}-\left(-m\right)$$

Subtracting -m from itself leaves 0.

$$k=\frac{n^{2}}{m^{2}}-\left(-m\right)$$

Subtract -m from \frac{n^{2}}{m^{2}}.

$$k=m+\frac{n^{2}}{m^{2}}$$