Solve y=sqrt{xy}

$$y= \sqrt{ xy }$$

Solve for x

$$\left\{\begin{matrix}x=y\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{xy}=y$$

Square both sides of the equation.

$$yx=y^{2}$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide y^{2} by y.

$$x=y$$

Solve for x (complex solution)

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

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=x\text{, }&arg(x)<\pi \text{ or }x=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=x\text{, }&x\geq 0\end{matrix}\right.$$