Solve y=1/3sqrt{x}

$$y= \frac{ 1 }{ 3 } \sqrt{ x }$$

Solve for x

$$x=9y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\frac{1}{3}\sqrt{x}=y$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}\sqrt{x}}{\frac{1}{3}}=\frac{y}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$\sqrt{x}=\frac{y}{\frac{1}{3}}$$

Divide y by \frac{1}{3} by multiplying y by the reciprocal of \frac{1}{3}.

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

Square both sides of the equation.

$$x=9y^{2}$$

Solve for x (complex solution)

$$x=9y^{2}$$

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

Solve for y (complex solution)

$$y=\frac{\sqrt{x}}{3}$$

Solve for y

$$y=\frac{\sqrt{x}}{3}$$

$$x\geq 0$$