Solve y=sqrt{2x/10}

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

Solve for x

$$x=5y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Divide 2x by 10 to get \frac{1}{5}x.

$$y=\sqrt{\frac{1}{5}x}$$

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

$$\sqrt{\frac{1}{5}x}=y$$

Square both sides of the equation.

$$\frac{1}{5}x=y^{2}$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{y^{2}}{\frac{1}{5}}$$

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

$$x=\frac{y^{2}}{\frac{1}{5}}$$

Divide y^{2} by \frac{1}{5} by multiplying y^{2} by the reciprocal of \frac{1}{5}.

$$x=5y^{2}$$

Solve for x (complex solution)

$$x=5y^{2}$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$y=\frac{\sqrt{5x}}{5}$$

Solve for y

$$y=\frac{\sqrt{5x}}{5}$$

$$x\geq 0$$