Solve sqrt{x*y}=z

$$\sqrt{ x \times y } =z$$

Solve for x

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

Steps for Solving Radical Equations

Square both sides of the equation.

$$yx=z^{2}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{z^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{z^{2}}{y}$$

Solve for y

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

Steps for Solving Radical Equations

Square both sides of the equation.

$$xy=z^{2}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{z^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{z^{2}}{x}$$

Solve for x (complex solution)

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

Solve for y (complex solution)

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