Solve {left(sqrt{x}sqrt{y}right)}^2=10y^2

$${ \left( \sqrt{ x } \sqrt{ y } \right) }^{ 2 } =10 { y }^{ 2 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=10y\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Expand \left(\sqrt{x}\sqrt{y}\right)^{2}.

$$\left(\sqrt{x}\right)^{2}\left(\sqrt{y}\right)^{2}=10y^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$x\left(\sqrt{y}\right)^{2}=10y^{2}$$

Calculate \sqrt{y} to the power of 2 and get y.

$$xy=10y^{2}$$

The equation is in standard form.

$$yx=10y^{2}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{10y^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{10y^{2}}{y}$$

Divide 10y^{2} by y.

$$x=10y$$

Solve for x

$$\left\{\begin{matrix}x\geq 0\text{, }&y=0\\x=10y\text{, }&y>0\end{matrix}\right.$$

Steps for Solving Linear Equation

Expand \left(\sqrt{x}\sqrt{y}\right)^{2}.

$$\left(\sqrt{x}\right)^{2}\left(\sqrt{y}\right)^{2}=10y^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$x\left(\sqrt{y}\right)^{2}=10y^{2}$$

Calculate \sqrt{y} to the power of 2 and get y.

$$xy=10y^{2}$$

The equation is in standard form.

$$yx=10y^{2}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{10y^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{10y^{2}}{y}$$

Divide 10y^{2} by y.

$$x=10y$$

Solve for y (complex solution)

$$y=\frac{x}{10}$$

$$y=0$$

Solve for y

$$y=\frac{x}{10}$$

$$y=0\text{, }x\geq 0$$