Solve T=2pisqrt{L/g^4}

$$T = 2 \pi \sqrt { \frac { L } { g ^ { 4 } } }$$

Solve for L

$$L=\frac{\left(\frac{T}{\pi }\right)^{2}g^{4}}{4}$$

$$T\geq 0\text{ and }g\neq 0$$

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{L}{g^{4}}}=T$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{g^{4}}L}}{2\pi }=\frac{T}{2\pi }$$

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

$$\sqrt{\frac{1}{g^{4}}L}=\frac{T}{2\pi }$$

Square both sides of the equation.

$$\frac{1}{g^{4}}L=\frac{T^{2}}{4\pi ^{2}}$$

Divide both sides by g^{-4}.

$$\frac{\frac{1}{g^{4}}Lg^{4}}{1}=\frac{T^{2}}{4\pi ^{2}\times \frac{1}{g^{4}}}$$

Dividing by g^{-4} undoes the multiplication by g^{-4}.

$$L=\frac{T^{2}}{4\pi ^{2}\times \frac{1}{g^{4}}}$$

Divide \frac{T^{2}}{4\pi ^{2}} by g^{-4}.

$$L=\frac{T^{2}g^{4}}{4\pi ^{2}}$$

Solve for T

$$T=\frac{2\pi \sqrt{L}}{g^{2}}$$

$$g\neq 0\text{ and }L\geq 0$$