Solve g=sqrt{xy}

$$g = \sqrt { x y }$$

Solve for x

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

Steps for Solving Radical Equations

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

$$\sqrt{xy}=g$$

Square both sides of the equation.

$$yx=g^{2}$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Solve for x (complex solution)

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

Solve for g

$$g=\sqrt{xy}$$

$$\left(y\geq 0\text{ and }x\geq 0\right)\text{ or }\left(x\leq 0\text{ and }y\leq 0\right)$$