Manipulating equations question In the equation: $$T = 2\pi \sqrt {\frac lg}$$
it is for determining period of pendulum swing
If I want to solve for $g$ and I want to start by removing the root
do I square everything in the equation, on just the left hand side?
thank you
 A: If two things are equal, for example $A=B$, then whatever we do on the left-hand side (LHS) we have to do on the right-hand side (RHS), otherwise they are not equal anymore, e.g. $A = B \rightarrow A^2 = B^2$ or $A+3=B+3$. So yes, you have to square both sides. Given this, can you give an expression for $g$?
A: You can square both sides and the equality will hold as long as both original numbers are positive
 $T^2 = 2^2 \pi^2 \sqrt{\frac{l}{g}}^2$ 
A: For $T,g\neq 0$ we have
 $$T = 2\pi \sqrt {\frac lg}\overset{(1)}{\implies}  T^2 = \left(2\pi \sqrt {\frac lg}\right)^2=4\pi^2 \frac lg \overset{(2)}{\implies} g = \frac{4\pi^2l}{T^2}$$
(1) square both sides of the equation.
(2) divide both sides of the equation by $T^2$ (this is why we need $T\neq 0$) and multiply both sides by $g$.
A: Notice, in order to get the value of $g$ $$T = 2\pi \sqrt {\frac lg}$$ $$(T)^2 =\left( 2\pi \sqrt {\frac lg}\right)^2$$ $$T^2 =4\pi^2\frac{l}{g}$$ $$\bbox[5px, border: 2px solid #C0A000]{\color{red}{g=\frac{4\pi^2l}{T^2}}}$$
Now, in order to calculate the acceleration due to Earth's gravity at particular point, substitute the time period $T$ & length of pendulum $l$ in the above relation.   
