# Binomial expansion with n=1/2

Is it possible to do a binomial expansion of $(x+y)^{1/2}$? I tried to compute it with the factorial expression for the binomial coefficients, but the second term already has n=1/2 and k=1, which makes the calculation for the binomial coefficient (n 1) weird, I think.

You may want to look at something like
http://en.wikipedia.org/wiki/Binomial_series

Assuming neither x or y are zero (and both are positive), I would recommend factoring out the larger of x or y and let your task reduce to that of finding $(1+z)^{1/2}$ with $z<1$.

For example, assume $y < x$, then your expression would be

$$f = \sqrt{x}\,(1+z)^{1/2}$$

Expand $(1+z)^{1/2}$ using the binomial series. The expansion will be an infinite series due to the non-integer exponent.