Solve v=sqrt{r/16}

$$v = \sqrt { \frac { r } { 16 } }$$

Solve for r

$$r=16v^{2}$$

$$v\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{\frac{r}{16}}=v$$

Square both sides of the equation.

$$\frac{1}{16}r=v^{2}$$

Multiply both sides by 16.

$$\frac{\frac{1}{16}r}{\frac{1}{16}}=\frac{v^{2}}{\frac{1}{16}}$$

Dividing by \frac{1}{16} undoes the multiplication by \frac{1}{16}.

$$r=\frac{v^{2}}{\frac{1}{16}}$$

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

$$r=16v^{2}$$

Solve for r (complex solution)

$$r=16v^{2}$$

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

Solve for v (complex solution)

$$v=\frac{\sqrt{r}}{4}$$

Solve for v

$$v=\frac{\sqrt{r}}{4}$$

$$r\geq 0$$