Solve T=2pisqrt{L/a}

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

Solve for L

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

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

Steps for Solving Radical Equations

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

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

Divide both sides by 2\pi .

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

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

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

Square both sides of the equation.

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

Divide both sides by a^{-1}.

$$\frac{\frac{1}{a}La}{1}=\frac{T^{2}}{4\pi ^{2}\times \frac{1}{a}}$$

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

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

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

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

Solve for L (complex solution)

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

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

Solve for T (complex solution)

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

$$a\neq 0$$

Solve for T

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

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