Solve T=2pisqrt{L/G}

$$T = 2 \pi \sqrt { \frac { L } { G } }$$

Solve for L

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

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

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{L}{G}}=T$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{G}L}}{2\pi }=\frac{T}{2\pi }$$

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

$$\sqrt{\frac{1}{G}L}=\frac{T}{2\pi }$$

Square both sides of the equation.

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

Divide both sides by G^{-1}.

$$\frac{\frac{1}{G}LG}{1}=\frac{T^{2}}{4\pi ^{2}\times \frac{1}{G}}$$

Dividing by G^{-1} undoes the multiplication by G^{-1}.

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

Divide \frac{T^{2}}{4\pi ^{2}} by G^{-1}.

$$L=\frac{GT^{2}}{4\pi ^{2}}$$

Solve for G

$$\left\{\begin{matrix}G=4\times \left(\frac{\pi }{T}\right)^{2}L\text{, }&T>0\text{ and }L\neq 0\\G\neq 0\text{, }&L=0\text{ and }T=0\end{matrix}\right.$$