Solve y=4sqrt{x/2}

$$y = 4 \sqrt { \frac { x } { 2 } }$$

Solve for x

$$x=\frac{y^{2}}{8}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$4\sqrt{\frac{x}{2}}=y$$

Divide both sides by 4.

$$\frac{4\sqrt{\frac{1}{2}x}}{4}=\frac{y}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\sqrt{\frac{1}{2}x}=\frac{y}{4}$$

Square both sides of the equation.

$$\frac{1}{2}x=\frac{y^{2}}{16}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{y^{2}}{\frac{1}{2}\times 16}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x=\frac{y^{2}}{\frac{1}{2}\times 16}$$

Divide \frac{y^{2}}{16} by \frac{1}{2} by multiplying \frac{y^{2}}{16} by the reciprocal of \frac{1}{2}.

$$x=\frac{y^{2}}{8}$$

Solve for x (complex solution)

$$x=\frac{y^{2}}{8}$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 0$$