Binomial Expansion Help?

L = h ( l ( l + 1 ) ) ^ (1/2)

Take out the factor l from the inner brackets.

L = h ( l^2 ( 1 + (1/l) ) ) ^ (1/2)

Take out the factor l^2 remembering to do (l^2)^(1/2) = l

L = hl ( 1 + (1/l) ) ^ (1/2)

for l>1, 1/l<1 so we can approximate with the binomial expansion to the first term of (1+x)^(1/2) = 1 + (1/2)x for x=1/l.

L = hl ( 1 + (1/2)(1/l) ) = h ( l + 1/2 )