Solve V=4pisqrt{x/4}

$$V = 4 \pi \sqrt { \frac { x } { 4 } }$$

Solve for x

$$x=\frac{\left(\frac{V}{\pi }\right)^{2}}{4}$$

$$V\geq 0$$

Steps for Solving Radical Equations

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

$$4\pi \sqrt{\frac{x}{4}}=V$$

Divide both sides by 4\pi .

$$\frac{4\pi \sqrt{\frac{1}{4}x}}{4\pi }=\frac{V}{4\pi }$$

Dividing by 4\pi undoes the multiplication by 4\pi .

$$\sqrt{\frac{1}{4}x}=\frac{V}{4\pi }$$

Square both sides of the equation.

$$\frac{1}{4}x=\frac{V^{2}}{16\pi ^{2}}$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{V^{2}}{\frac{1}{4}\times 16\pi ^{2}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$x=\frac{V^{2}}{\frac{1}{4}\times 16\pi ^{2}}$$

Divide \frac{V^{2}}{16\pi ^{2}} by \frac{1}{4} by multiplying \frac{V^{2}}{16\pi ^{2}} by the reciprocal of \frac{1}{4}.

$$x=\frac{V^{2}}{4\pi ^{2}}$$

Solve for V (complex solution)

$$V=2\pi \sqrt{x}$$

Solve for x (complex solution)

$$x=\frac{\left(\frac{V}{\pi }\right)^{2}}{4}$$

$$|\frac{arg(V^{2})}{2}-arg(V)|<\pi \text{ or }V=0$$

Solve for V

$$V=2\pi \sqrt{x}$$

$$x\geq 0$$