Solve alpha=sqrt{k/c}

$$\alpha = \sqrt { \frac { k } { c } }$$

Solve for k

$$k=c\alpha ^{2}$$

$$\alpha \geq 0\text{ and }c\neq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{k}{c}}=\alpha$$

Square both sides of the equation.

$$\frac{1}{c}k=\alpha ^{2}$$

Divide both sides by c^{-1}.

$$\frac{\frac{1}{c}kc}{1}=\frac{\alpha ^{2}c}{1}$$

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

$$k=\frac{\alpha ^{2}c}{1}$$

Divide \alpha ^{2} by c^{-1}.

$$k=c\alpha ^{2}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{k}{\alpha ^{2}}\text{, }&\alpha >0\text{ and }k\neq 0\\c\neq 0\text{, }&k=0\text{ and }\alpha =0\end{matrix}\right.$$