Solve sqrt{x/y}=y

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

Solve for x

$$x=y^{3}$$

$$y>0$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$\frac{1}{y}x=y^{2}$$

Divide both sides by y^{-1}.

$$\frac{\frac{1}{y}xy}{1}=\frac{y^{2}y}{1}$$

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

$$x=\frac{y^{2}y}{1}$$

Divide y^{2} by y^{-1}.

$$x=y^{3}$$

Solve for x (complex solution)

$$x=y^{3}$$

$$arg(y)<\pi \text{ and }y\neq 0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\sqrt[3]{x}\text{, }&x\neq 0\\y=e^{\frac{2\pi i}{3}}\sqrt[3]{x}\text{, }&x\neq 0\text{ and }arg(e^{\frac{2\pi i}{3}}\sqrt[3]{x})<\pi \\y=e^{\frac{4\pi i}{3}}\sqrt[3]{x}\text{, }&arg(e^{\frac{\pi i}{3}}\sqrt[3]{x})\geq \pi \text{ and }x\neq 0\end{matrix}\right.$$

Solve for y

$$y=\sqrt[3]{x}$$

$$x>0$$