Solve v=sqrt{2a*s}

$$v = \sqrt { 2 a \cdot s }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{v^{2}}{2s}\text{, }&v\geq 0\text{ and }s\neq 0\\a\in \mathrm{R}\text{, }&s=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{2as}=v$$

Square both sides of the equation.

$$2sa=v^{2}$$

Divide both sides by 2s.

$$\frac{2sa}{2s}=\frac{v^{2}}{2s}$$

Dividing by 2s undoes the multiplication by 2s.

$$a=\frac{v^{2}}{2s}$$

Solve for s

$$\left\{\begin{matrix}s=\frac{v^{2}}{2a}\text{, }&v\geq 0\text{ and }a\neq 0\\s\in \mathrm{R}\text{, }&a=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{2as}=v$$

Square both sides of the equation.

$$2as=v^{2}$$

Divide both sides by 2a.

$$\frac{2as}{2a}=\frac{v^{2}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$s=\frac{v^{2}}{2a}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{v^{2}}{2s}\text{, }&s\neq 0\text{ and }\left(v=0\text{ or }arg(v)<\pi \right)\\a\in \mathrm{C}\text{, }&v=0\text{ and }s=0\end{matrix}\right.$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=\frac{v^{2}}{2a}\text{, }&a\neq 0\text{ and }\left(v=0\text{ or }arg(v)<\pi \right)\\s\in \mathrm{C}\text{, }&v=0\text{ and }a=0\end{matrix}\right.$$