Solve y=2pisqrt{L/32}

$$y = 2 \pi \sqrt { \frac { L } { 32 } }$$

Solve for L

$$L=8\times \left(\frac{y}{\pi }\right)^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{L}{32}}=y$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{32}L}}{2\pi }=\frac{y}{2\pi }$$

Dividing by 2\pi undoes the multiplication by 2\pi .

$$\sqrt{\frac{1}{32}L}=\frac{y}{2\pi }$$

Square both sides of the equation.

$$\frac{1}{32}L=\frac{y^{2}}{4\pi ^{2}}$$

Multiply both sides by 32.

$$\frac{\frac{1}{32}L}{\frac{1}{32}}=\frac{y^{2}}{\frac{1}{32}\times 4\pi ^{2}}$$

Dividing by \frac{1}{32} undoes the multiplication by \frac{1}{32}.

$$L=\frac{y^{2}}{\frac{1}{32}\times 4\pi ^{2}}$$

Divide \frac{y^{2}}{4\pi ^{2}} by \frac{1}{32} by multiplying \frac{y^{2}}{4\pi ^{2}} by the reciprocal of \frac{1}{32}.

$$L=\frac{8y^{2}}{\pi ^{2}}$$

Solve for L (complex solution)

$$L=8\times \left(\frac{y}{\pi }\right)^{2}$$

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

Solve for y (complex solution)

$$y=\frac{\pi \sqrt{2L}}{4}$$

Solve for y

$$y=\frac{\pi \sqrt{2L}}{4}$$

$$L\geq 0$$