Transmission line approximation 1. The problem statement, all variables and given/known data In the derivation of the approximate formulas of \gamma and Z0 for low loss lines, all terms containing the second and higher order powers of R/wL and G/wC were neglected in comparison with unity. (R/wL<<1 and G/wC<<1) gamma=jw*sqrt(LC)*sqrt(1+R/jwL)*sqrt (1+G/jwC) approximated to gamma = jw*sqrt(LC)*(1+R/2jwL)*sqrt(1+G/2jwC) gamma is the propagation constant which is equal to alpha+j beta At lower frequencies, better approximation may be required. find new formulas for \gamma and Z0 for low loss lines that retain terms containing (R/wL)^2 and (G/wL)^2 2. Relevant equations Required result is alpha = sqrt(LC/2)*(R/L+G/C)*[1-(1/8w^2)*(R/L-G/C)^2] beta = w*sqrt (LC)*[1+(1/8w^2)*(R/L-G/C)^2] 3. The attempt at a solution I tried expanding the term sqrt(1+R/jwL) using square root expansion : 1+(1/2)*R/jwL-(1/8)*(R/jwL)^2 did the same for sqrt (1+G/jwC) I am unable to get the desired result. Any help. FYI, this is prob 9.7 in cheng.