Solve r=sqrt{A/3}

$$r = \sqrt { \frac { A } { 3 } }$$

Solve for A

$$A=3r^{2}$$

$$r\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{\frac{A}{3}}=r$$

Square both sides of the equation.

$$\frac{1}{3}A=r^{2}$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}A}{\frac{1}{3}}=\frac{r^{2}}{\frac{1}{3}}$$

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

$$A=\frac{r^{2}}{\frac{1}{3}}$$

Divide r^{2} by \frac{1}{3} by multiplying r^{2} by the reciprocal of \frac{1}{3}.

$$A=3r^{2}$$

Solve for A (complex solution)

$$A=3r^{2}$$

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

Solve for r (complex solution)

$$r=\frac{\sqrt{3A}}{3}$$

Solve for r

$$r=\frac{\sqrt{3A}}{3}$$

$$A\geq 0$$