How do I calculate the percentage error of this?

I am given an equation for the period of a pendulum



T=2*pi*(L/G)^.5



If L and G have a respective percentage error of 0.2% and 0.6% how do I go about evaluating the maximum percentage error of T?

Any advice that anyone can give is greatly appreciatedHow do I calculate the percentage error of this?
ε? = 0.002, ε? = 0.006

Let's consider the worst case: L'=L(1+ε?), G'=G(1-ε?). Then L'/G' ≈ L/G*(1+ε?)(1+ε?) because (1+α)^n ≈ 1+nα when α?1. Now, (1+ε?)(1+ε?) ≈ 1+ε?+ε? (we can neglect ε?ε? here). Again, √(L'/G') ≈ √(L/G*(1+ε?+ε?)) ≈ √(L/G) * (1+ (ε?+ε?)/2). So percentage error is ((1+(ε?+ε?)/2)-1)/1 = (ε?+ε?)/2 = 0.004 = 0.4%



I advise you to read something like 3rd chapter of Taylor 'An introduction to error analysis' (you can find that on Google Books).