Solve T=2pisqrt{R/g}

$$T = 2 \pi \sqrt { \frac { R } { g } }$$

Solve for R

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

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

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{R}{g}}=T$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{g}R}}{2\pi }=\frac{T}{2\pi }$$

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

$$\sqrt{\frac{1}{g}R}=\frac{T}{2\pi }$$

Square both sides of the equation.

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

Divide both sides by g^{-1}.

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

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

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

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

$$R=\frac{gT^{2}}{4\pi ^{2}}$$

Solve for R (complex solution)

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

$$g\neq 0\text{ and }\left(T=0\text{ or }|\frac{arg(T^{2})}{2}-arg(T)|<\pi \right)$$

Solve for T (complex solution)

$$T=2\pi \sqrt{\frac{R}{g}}$$

$$g\neq 0$$

Solve for T

$$T=2\pi \sqrt{\frac{R}{g}}$$

$$\left(R\geq 0\text{ and }g>0\right)\text{ or }\left(R\leq 0\text{ and }g<0\right)$$